It is, however, a fact not a theory, that Elo's system predicts that the probability of winning losing or drawing is dependant only on the rating difference between the two players.
I dont think Fide-ELO is a prediction. It is used to divide players into classes, but its not a prediction. ELO is summing up results from the past, and tells how strong the players have been.
My Elo is based on how good I was as a beginner this winter, and increased when better results ticked in this autumn. It is not the same as my latest results (which more accurately describes my new strenght), but it is between my late results and my winterresults.
Players that has been on the same level for years do have Elo-rating that is describing their current strenght quite well.
Kids that is improving very fast are of course very underrated, because they are much stronger now , than they were back in August/September. I guess that todays Elo might describe quite close how good the player was in August.
I feel thatChess.com ratings are closer up to date, but they are also describing strenghts of the past, but a bit closer past.
I tend to think the difference between an 1800 and a 2300 is actually basically the same as the difference between an 1800 and a 1300, if we're going by, how badly/how likely we would expect one person to lose in a match, etc. Of course, the increase in knowledge needed to jump from 1300 to 1800 is totally different from that needed to jump from 1800 to 2300.
I think the elo system is one of those things that people are actually too sceptical of (usually people are not sceptical enough of things). This number changes with every single tournament game; it accounts for all the ups and downs; it accounts for all the clashes of style (and even the effect of this tends to be quite overestimated), etc etc. Sure, it's possible to manipulate the system a little bit if you only play four players dozens of times or something, but you really have to dig for exceptions to give problems for the rating system. Concerns about variability, psychology, etc, are really just accounted for -- those things affect your results, and those results go into your number, and thus the "prediction" for how you will do against your opponent. And predictions are guesses of course, sometimes right and sometimes wrong, but those predictions are very well grounded when it comes to the rating system.
Maybe it's because people don't like to be summarized by a number. They want to wiggle their way out of a label, like they can often do. Unfortunately for them, their rating is actually quite objective and not at all easy to explain away. Yeah, I perform better as a chess player than you if I have a clearly higher rating than you, no matter how much you don't "care for" my play. Of course people can improve, and maybe their rating hasn't "caught up" to their improvement, but measuring how high their rating "should be" tends to be extremely biased and in most cases is not as reliable as simply looking at the rating they already have.