Magnus Carlsens title is that of the World chess champion. A world championship cycle happens currently every 2 years (with 2020 delayed due to covid) and he does the title defense regardless of the amount of games he played in those years. (Since you clearly didnt want to read up on that before posting, here a link to make up for that: https://en.wikipedia.org/wiki/World_Chess_Championship)
That first obvious point (he does not have to play a single game at all to be able to defend his title) out of the way - why does he play many tourneys & games regardless? He thinks it trains him (earlier champs used to be less active in their title defense years btw). He would be outclassed because the others dont slack if he doesnt play at all and also arent incredibly much weaker (Another interesting link for you: https://2700chess.com - the difference between top 1 and top 50 isnt 600+ points like on FAF).
To your next point, which is also inccorect. They do not invite only the top active players. A great example is the St. Louis which marked Kasparovs temporary comeback to professional chess - funny that you even mention him as not being able to be invited, when that is just what happened (https://www.chess.com/news/view/carlsen-kasparov-saint-louis-chess-chess960). Same thing goes for Karpov/Kramnik who have a trivial time getting invitations whenever they wish to play a tourney (https://en.chessbase.com/post/anand-vs-kramnik-no-castling, just 3 days ago, even catering to Kramniks favourite playing variant). The reason those people are not in the tourneys is because they do not want to play.
Then, to make it even more obvious how incorrect your statement is and because you picked it as an example: If you win the TATA you get invited back the next year. This is the same distance in time as there is between 2 LOTS. Also added on that, if you win your group in the TATA, you get moved up and automatically invited the next year (this happens to every chess prodigy rising up the ranks). So yes, chess works exactly as I stated and nothing like you think it does. All of what I wrote here can be trivially fact-checked where I didnt already provide the links myself, so feel free to do so.
Adding up, Magnus does not beat 2500 players in tourneys "all the time". If you would check his tourneys and games (as I do, a link for you to do so as well https://2700chess.com/players/carlsen), you will see that in serious competition (Banter blitz is not serious competition, neither are lichess titled arenas) he very rarely plays a player more than ~150 rating points apart from himself. In fact, some upcoming GMs even complain about this due to thinking they dont get enough chance to compete against him.
Anything else? Ah yeah. The majority of the big chess tourneys (including almost all of the ones you mentioned) are invite-only with ~2 wildcards mixed in. In fact I even disagree with this because I think you should have qualifying chances in some way (even if it is just rating).
So in sum: Your post is mostly incorrect and borderline intellectually insulting. I didnt pick my examples because they are blatantly wrong.