Why didn't Fischer play Karpov

Fischer wasn't a fugitive until after the 90s Spassky match. The match where he became world champ was played in the 70s.
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I imagine Fischer didn't play Karpov for the same reason he very nearly didn't play Spassky... partly fear of losing, and partly fear of winning. If he loses it's proof he's not as good... but even worse, If he wins and he's the best, in a way his life loses it's meaning (working towards that goal is what kept him going).

Your questions sound like something straight out of the Cold War era.
Back then, Chess Life magazine waged a propaganda war against the Russians, casting Bobby Fischer as protagonist/hero versus Anatoly Karpov, cast as antagonist/villain, supposedly assisted by a host of Russian minions while Bobby supposedly got no help whatsoever. As they say, the first casualty of war is the truth.
The fact remains that FIDE has a process through which it selects the world champion, and at the time Karpov emerged, Bobby didn't want any part of it. For one thing, FIDE gets a piece of the action-- some of the money the title match earns. No way, thought Bobby. For another thing, FIDE dictates the terms (i.e. the process). Again, no way-- not gonna happen.
On top of this, Bobby was not a good loser. He darn near pulled out of the 1972 match when Spassky beat him (once again). Ironically, this championship match turned into precisely the kind of farce which has so often been associated with the Karpov vs. Kortchnoi match, except that nobody was physically held hostage.
The real question is, why didn't Fischer play competitive chess for twenty years, after he was annointed the 1972 FIDE world champion? (Note how, with the Cold War propaganda nonsense nixed, Karpov is irrelevant.)
I think a clue to solving this puzzle can be found in Bobby's choice of opponent, when he finally decided to "cash in" in 1992 by playing once again. He did not choose to play Kasparov. Or Karpov. Or anybody who he was not pretty certain he could thrash. I wish he had picked me, offering pawn odds, then two pawns, a Knight, a Bishop, a Rook, two pieces, a Queen, etc. First to win six games. It would have been a tough match... .

I remember reading an article back in 1975 that Charles Kalme wrote who was a very good chess player and a mathematician. He proved that the challenger in fact had a better chance than the old 24 game fixed match.
Yes the FIDE was "controlled" by Russia back then and still is.
Karpov when he went to defend his title that was won without and games had everything Fischer ever wanted, they had no problem giving it to him.
Fischer would have destroyed Karpov in my opinion at the time. he was that much better than anyone else and probably would have held the title for about 8 years, Kasparov would have broken through and beat him when Fischer got older but no one before him.

I read match of the century back then, I barely remember it though. It did say that Fischer mainly refused because he felt Top chess players should be compensated more, so he boycotted tournament chess. Which in my opinion hurt the chances of more Americans becoming involved with chess. At least for a couple decades.
I am not saying Fischer wasn't right, because when he did that, the smear campaign began on his mental health. Also the title should have reverted back to Spassky, but Spassky was tossed aside like a used up tissue, which is a great loss to chess. I met Spassky, and he was a fantastic person, not to mention an incredible player.

Just my opinion...
He had spent his life preparing to defest the Russian chess machine, to become the best, and to improve conditions at tournaments. When he beat Spassky, there was a man at 32, that felt he had nothing left to accomplish.

From what I saw, Fischer was in fear of losing an early game and then Karpov forcing every subsequent game to a draw because of the advance of theory.
Therefore he wanted a "first to 10 wins" tournament, and they actually agreed except that he wanted a clause that if it went to 9-9 he would retain his status as champion. That meant Karpov would have to win by a 2-game margin (10-8) and the authorities did not agree to that.
For the 1978 world championship they went partly along with Fischer's idea too, but only first to 6 wins. And the match did go to 5-5 at one point, then Karpov won to win it.
In 1972, Fischer had come back from a 2-game deficit, having lost the first game stupidly, and the second by default. By game 5 he was level at 2-2.
And having established a big lead, there was then a long series of drawn games. So he was right in a sense about the possibility of a long series of draws to take the match to its conclusion.

I saw a documentary on Discovery channel about the matches Karpov - Kasparov. Karpov had a hypnotist as assistant - they gave his name but I don't remember it. Fischer feared such persons.

I think Bobby was scared of Karpov, not because he was Russian but because he was the new young high energy level player and Bobby thru his career had always been the younger player 99% of the time, and this hurt his mentality. He knew he had reached the top and he was scared that when he lost it would damage his reputation.
In his own mind he wanted to be "the best" forever but he knew that this was an impossible task.
You show a guess (I think...), I show fact. It seems that few know the story of RJ Fischer these days. But you can read on Wikipedia. It was there the last time I've checked.
I know that story. Karpov had a hypnotist in audience and Kasparov thought that the hypnotist was sending Karpov signals through the youghurt. Therefore Karpov was banned from eating yoghurt for the rest of the match.
In case you're not joking, you're thinking of the Korchnoi match.

However, Kasparov was convinced Karpov's aides were giving him both drugs and secret messages through yogurt.

Yes, Dr. Zukhar (a well known hypnotist) - see https://en.wikipedia.org/wiki/World_Chess_Championship_1978
That's why Fischer didn't even consider to play against Karpov.

Why didn't Fischer ever play Karpov in tournaments or for the world title ?
Why didn't FIDE force Karpov to play the match? and why did FIDE instead let Karpov be the world champion. Was FIDE a company owned by the former USSR ?
Just my own uneducated opinion.
The man spent his life, and chess career obsessed with two things. Being the world champion, and defeating the Russian chess machine. Once he won the title, he must have felt like there was nothing else to do in life. No wonder the poor man went off the deep end.
I cant imagine being so obsessed over something that once you accomplished that life goal, you felt you had nothing else to live for.
Why didn't Fischer ever play Karpov in tournaments or for the world title ?
Why didn't FIDE force Karpov to play the match? and why did FIDE instead let Karpov be the world champion. Was FIDE a company owned by the former USSR ?