I just watched the first couple of minutes and I'm speechless
Disgusting Video

Yeah, it would probably be better to remove all living or active players (but you can keep former world champs on the list like Kasparov, Kramnik, and Anand).
But if you are going to include living / active players, then Naka probably shouldn't be on the list at all.
You can replace him with great players of the past.
I wanted to remove Caruana from the list with the same reasoning as you had in your post, but decided against it because he will most likely deserve to be on the list when he ends his career, so I didn't want to complicate my post too much.

Suppose the off-chance possibility that respectable players collectively agree that Nakamura is indeed a stronger chess player than Caruana. I still think that it is wrong to ask a popular International Master to rank you as a "god of chess" and simply agree with him when he gives you the opportunity to object.
I vaguely remember once watching an American football video where Joe Montana didn't even rank himself among the top 5 quarterbacks in history. That is humbleness. What Hikaru did is not.
Don't get me wrong. I'm a huge fan of Hikaru. His Youtube videos are great. He's a genius and sparked tons on interest chess and new arrivals to the game with his Twitch and Youtube presence. But as it has quite a few times before, his ego got ahead of him here.

the chat was going bonkers, saying "no no no no" and "weird flex weird flex". Mixed reactions I suppose.

At around 52:35 in the video, Hikaru humbly puts himself from the tier of "God of chess" to "Legends" if anyone didn't notice. I think everyone in this forum can agree that's a reasonable place to put himself


I just noticed, hikaru wasn't online for more than 24 hours, maybe he is ashamed and decided to quit chess.com?
Who would miss watching his bliz games?
If it's you then you probably think he is a pro, which he sorta is, but less that he is a show off
He is a super gm in standard, admit it, alse he is a super pro at showing off.

I mean, considering that online chess is the future, and considering Naka is the most dominant online chess player to date, I doubt that.

At around 52:35 in the video, Hikaru humbly puts himself from the tier of "God of chess" to "Legends" if anyone didn't notice. I think everyone in this forum can agree that's a reasonable place to put himself

Hikaru is incredibly arrogant imo. You can just tell from his recent game where he Bongclouded against GM Jeffrey Xiong.
I don't think he was trying to be disrespectful to Xiong in particular. However, I think that him going for the bongcloud was an obvious attempt for him to gain popularity and controversy.

At around 52:35 in the video, Hikaru humbly puts himself from the tier of "God of chess" to "Legends" if anyone didn't notice. I think everyone in this forum can agree that's a reasonable place to put himself
Why? He crossed 2800 briefly, peaked at #2, and went to one candidates tournament.
Other players that aren't on the list have done that. As someone mentioned here, Mamedyarov did exactly those things... and finished better in his Candidates tournament than Naka did.
Mamedyarov's peak rating is > Nakamura's peak rating too.
So surely Mamedyarov is a legend too?
lol

I mean, considering that online chess is the future, and considering Naka is the most dominant online chess player to date, I doubt that.
Most dominant online player?
Cough cough* he recently lost in the finals to Carlsen cough cough*
Sure it was in armageddon and so Naka proved once again that the only question about his speed chess rank is whether it's #1 or #2.
But dominant? Above who? Carlsen doesn't play on chess.com.

Did ANYONE watch to the moment where hikaru moved himself to legend?
It's around 52:20
My OP doesn't mention God of Chess rank. It mentions his comments about how he was a serious world champ contender (he wasn't), and rating himself above Caruana, which is ridiculous.
I know he wants to substitute Twitch followers for rating points, but then as I said, why isn't xQc ranked up there with Anand?
In other words he surreptitiously (and rather shamelessly) chose the criteria which were most favorable to himself.
Caruana played in the world championship match and was in the press e.g.
https://www.nytimes.com/2018/11/03/sports/bobby-fischer-chess-caruana.html
But the New York Times isn't Twitter is it? So Naka rates himself higher.
Yeah, it would probably be better to remove all living or active players (but you can keep former world champs on the list like Kasparov, Kramnik, and Anand).
But if you are going to include living / active players, then Naka probably shouldn't be on the list at all.
You can replace him with great players of the past.