Leela, such a great engine (and innovation)?

[Dann Corbit]

I think it was clear who was the best in several time periods (even if, as you said, it didn't coincide with who was champion), and we didn't need hundreds of thousands of games to know.

I have never said one hundred thousand games are necessary. If there is decent separation in the real strength a couple thousand games is plenty.

So, are you saying that the only times we were able to know who was the best human player were those where the separation between them and second best was big enough that the games that they played in that time period were enough to know they were best?

I am saying that if two players are very nearly equal in ability it take a very large number of games to know which one is really strongest.
I am saying that our clever intuition about which one is strongest can be wrong.
I am saying that a better judge of strength is a contest where an enormous number of games is played.
I am saying that championships are also very interesting and that with a championship, the winner may or may not coincide with the strongest player.
I am saying that mathematics can tell us when our intuition meshes correctly with reality.

But your summary is also pretty good. Lots of games are very helpful to measure real strength and especially when the contestants are nearly equal.
It there is a big gap in strength (e.g. 300 Elo), then we don't need a huge number of games to know which is stronger.
But when the real strength is almost exactly equal, we don't really know which one is strongest most of the time.
True, we might guess right. And then again, we might not.
I do agree with your assessment that Carlsen is probably the strongest player in the world. In fact, I think he may be stronger than Kasparov was. But I do not know that for sure.