Well, you could argue, that it is Staunton that reminds of Fischer, as they both refused to play for the 'title'. It would have been a great match as Staunton was a tremendous player. But probably Morphys youth would have given him the laurells in the end. And Staunton probably feared that. Like Fischer probably feared the young Karpov.
Paul Morphy or Howard Staunton?
Morphy 2743 was stronger than Staunton 2706
http://www.chessmetrics.com/cm/CM2/PlayerProfile.asp?Params=199510SSSSS3S125695000000111000000000028210100
Morphy played chess as he had earned his law degree, but was not yet old enough to practice as a lawyer. When he was old enough to practice as a lawyer, he quit chess, but his carreer as a lawyer was not successful. This caused his trouble.
Morphy would have crushed Staunton. My favourite player from the 1800's is Adolph Anderssen. Botvinnik rules though. 🤔

I came across a book in the library once, written by Staunton. Think it was called "The chessplayer's handbook" or something.
thumbing through it almost made me crack up at the state of opening theory of the time.
For example, after the classic moves 1.e4 e5 2.d4 d4, Staunton claimed white's ONLY chance for an advantage, was 3.exd5
True. I think back then most players did what they were told as being "best" instead of just playing chess. Also they had this macho mentality of being a romantic and refusing a gambit was not manly. 🙄

Which is your favorite 1800's, unofficial world chess champion.
It is said that because Staunton refused to play Morphy, Morphy began to deteriate mentally.
As did Bobby Fischer, the only other American world champion in chess history.
Staunton devised the "English Opening" the best possible opening move for White.
https://www.365chess.com/opening.php?m=2&n=15&ms=c4&ns=15
First, Staunton's refusal to play had nothing to do with Morphy's mental state, though it may have had something to to with Morphy's growing distaste for and eventual abandonment of public chess.
Staunton was primarily noted as a writer (on chess and Shakespeare), analyst and organizer and during his heyday was the best at these things. Morphy, who really never explained anything, was the player supreme.
Morphy could never do what Staunton did and Staunton could never do as Morphy did.

Which is your favorite 1800's, unofficial world chess champion.
It is said that because Staunton refused to play Morphy, Morphy began to deteriate mentally.
As did Bobby Fischer, the only other American world champion in chess history.
Staunton devised the "English Opening" the best possible opening move for White.
https://www.365chess.com/opening.php?m=2&n=15&ms=c4&ns=15
First, Staunton's refusal to play had nothing to do with Morphy's mental state, though it may have had something to to with Morphy's growing distaste for and eventual abandonment of public chess.
Staunton was primarily noted as a writer (on chess and Shakespeare), analyst and organizer and during his heyday was the best at these things. Morphy, who really never explained anything, was the player supreme.
Morphy could never do what Staunton did and Staunton could never do as Morphy did.
Batgirl.
Do (or don't) you believe Staunton abused his position as chess editor, to duck Morphy?

Staunton was in the habit of using his magazine, particularly via anonymous letters to the editor, to advance himself and denigrate his enemy-of-the-week, but while his evasion of Morphy's challenge had an unsavory aspect, it also had reasons that were justified. Let's just say that Staunton was justified in not playing Morphy -and none of his reasons involved fear- but he went about it in the worst possible way. I think his character and personality made him unable to act otherwise.

Staunton actually did agree to play Morphy when Morphy challenged him to a match after demolishing the best American players at the first American Chess Congress in New York. Terms were arranged but Morphy's telegram confirming his acceptance, assuring Staunton that the prize fund was fully covered, and Morphy's projected arrival date never got to England due to a break in the trans-Alantic telegraph cable. While Morphy was sailing to England, Staunton got an offer to edit and annotate a new addition of Shakespeare's works, a large and well-paid job. Not having heard from Morphy, he accepted and didn't have time to play a chess match. (He had a deadline to meet.)
Staunton never claimed to be world chess champion (he did little to discourage the claim). This was the work of other English writers boosting England's pretension to be the greatest nation on earth, best at everything. He was the top player in England but didn't win top prize at any big international tournament.
Morphy was disappointed to have missed this match, but the chess activities he did undertake on this trip to Europe are legendary. Most of the chess world hailed him as the greatest player ever and he is usually considered the first--if unofficial--world champion.

Staunton actually did agree to play Morphy when Morphy challenged him to a match after demolishing the best American players at the first American Chess Congress in New York. Terms were arranged but Morphy's telegram confirming his acceptance, assuring Staunton that the prize fund was fully covered, and Morphy's projected arrival date never got to England due to a break in the trans-Alantic telegraph cable.
That's not quite accurate.
On Feb. 4, 1858 members of the N.O. Chess Club took it upon themselves to invite Staunton to come to New. Orleans for a match with Morphy for stakes of $5,000. Part of the terms provided that he would be reimbursed $1,000, should he lose, to cover expenses. According to Lawson, "Staunton was singled out for this challenge because, in the opinion of the committee, he was the most outstanding figure in English chess."
Anyway, Staunton, who probably viewed the challenge as presumptuous, replied rather graciously:
"Gentlemen:
In reply to your very courteous proposal for me to visit New Orleans for the purpose of encountering Mr. Paul Morphy at Chess, permit me to mention that for many years professional duties have compelled me to abandon the practice of the game almost entirely except in the most desultory manner, and at the present time these duties are so exacting that it is with difficulty I am enabled to snatch one day out of seven for exercise and relaxation.
Under the circumstances you will at once perceive that a long and arduous chess contest, even in this Metropolis, would be an enterprise too formidable for me to embark in without ample opportunity for the recovery of my old strength in play, together with such arrangements as would prevent the sacrifice of my professional engagements for the sake of a match at chess, and that the idea of undertaking one in a foreign country, many thousand miles from here, is admissible only in a dream.
With friendly greetings to my proposed antagonist, whose talent and enthusiasm no one can more highly estimate, and with compliments to you for the honor implied in your selection of me as the opponent of such a champion, I beg to subscribe myself, with every consideration.
Yours obediently,
H. Staunton"
At the same time Staunton, being Staunton, published the following in the Illustrated London News, where he had a chess column:
"if Mr. Morphy - for whose skills we entertain the highest admiration - be desirous to win his spurs among the chess chivalry of Europe, he must take advantage of his proposed visit next year; he will then meet in this country, in France, in Germany and in Russia, many champions whose names must be as household words to him, ready to test and do honor to his prowess."
Although Staunton doesn't explicitly accept the challenge, Morphy took this as an implication that Staunton would play him if he were the one to travel.
The problem really lies in that even if Staunton didn't intend this, he never once disavowed Morphy of this belief.
Morphy, who ostensibly went to England to take part in the Birmingham Meeting, never went to London with the idea that a match between him and Staunton had been arranged, but rather that he was willing to accede to all of Staunton's conditions to remove any barriers to his acceptance of a match (i.e. “ample opportunity for the recovery of my old strength in play, together with such arrangements as would prevent the sacrifice of my professional engagements”).
Playing or not playing Staunton in and of itself didn't seem to be of much concern to Morphy. But being forced to waste his limited time in Europe (and particularly being stuck in England when France was his main love) proved to be the thorn in his side.

A knowledgeable person reminded me that Staunton had begun his Shakespearean connection with Routledge long before Morphy sailed for Europe - in fact he had his first installment completed even before Morphy won the American Chess Congress tournament.

We don't know what Morphy and Staunton may have said to each other via telegraph but it seems Morphy thought a match had been agreed to, with only petty details to be ironed out once he reached England. And Staunton used the "I'm too busy with this Shakespeare project to play you now" excuse to put him off. Thanks for the further information.

Actually, it's quite clear that Morphy didn't seen a match arrangement with Staunton as a fait accompli but as a likelihood should he agree to Staunton's terms. The Shakespearean book was a primary source for Staunton's livelihood at that time. It's wasn't just some excuse. Staunton should have said upfront that he was too busy to prepare for a serious match (which he was), but he didn't. He left the possibility hanging in the air, keeping Morphy from other activities. By the time Staunton did admit he wouldn't be in a position to play, it had already turned ugly in the press.
Which is your favorite 1800's, unofficial world chess champion.
It is said that because Staunton refused to play Morphy, Morphy began to deteriate mentally.
As did Bobby Fischer, the only other American world champion in chess history.
Staunton devised the "English Opening" the best possible opening move for White.
https://www.365chess.com/opening.php?m=2&n=15&ms=c4&ns=15