I can't argue with your first premise. Your following points, however, are less convincing.
"Like Kasparov and Grischuk pointed out today, every other chess player gets worse playing rapid/blitz but Carlsen is the only one who actually improves."
Even if Kasparov and Grischuk said this today (citation please?), it doesn't make it true. There are many players who get better playing rapid and blitz. Look at the trajectory of the Bay Area's own GM Daniel Naroditsky. Nakamura.
I suspect most of the blitz haters are people who simply haven't spent enough time to get good at it.
"Regardless of all critics."
To your main point, the critics weren't saying that Carlsen isn't the best. They were complaining because he is not acting with respect to the purity and beauty of the game. There is simply an aesthetic ugliness to offering a draw with such a crushing time advantage in a better position.
I'm not arguing that this may not have been good strategy, lose the battle, win the war, etc etc.
What I'm saying is that there is a war to be won that is different than a 1 or 0 point. It's the battle for hearts and minds, which is won not just through victory but through integrity and courage. You win hearts by showing hearts.
Magnus didn't win hearts with his mercilessly pragmatic approach to winning the world championship title. I still respect him as the rightful owner of the title of best chess player in the world.
But if we're going to employ the "good by association" logical fallacy with whatever Kasparov and Grischuk may have said today, why not actually just quote the champion Magnus himself?
In the press conference, he came out and told everyone that Fabiano earned the right to share the crown of world's best player in classical chess with him.
Who am I, who are you, who are any of us to disagree with that?
I also enjoyed the final a lot. But the fact remains that the beauty and spectacle 2018 World Championships of the world's most beautiful mind game was marred by a decidedly un-beautiful game in round 12.