You're assuming a steady-state equilibrium. It takes several games for a player to settle into their Elo, and a cheater will have ruined the experience of their opponents in the meantime. You're also discounting the fact that griefers will deliberately create new accounts to continue playing against novice opponents.

How is this different from good (non-cheating) players joining a new website and having to get to their realistic rating? This happens, but as a percentage of games you play it has a very low impact; moreover, platforms usually tell you that a player has a not-yet-established rating with a question mark, eg 1620?

My suggestion is to just stop thinking about cheaters when playing online rated games. I started doing so years ago, and have increased my enjoyment of the game A LOT, without any visible downside.

Yeah seems like a trivial issue to fix - first 10 games are for evaluation, heck they can be had even against computer. Very few people are so pathetic/psychopathic to invest so much time into getting a rank and then cheating on real opponents and tank their account quickly. And for those few, just don't care about them, its just a game after all.