I think acceleration services started out with anyway self-promotional motivations. ViaBTC, for example, loaded up that "manifesto" page in the months prior to the Bitcoin Cash fork. They may have helped a lot of people who unwittingly used low fee transactions, but yeah, after all these free services became known, I think people just used them to skimp on fees. You could say this just delayed the application of "correct" behaviour when it comes to spending coins, in a way cheating others who actually use good fees and maintain good wallet practises.
As you say though, exchanges and other site-based wallets are themselves not using high-enough fees, and I can perfectly understand people use these acceleration services since they have no control over withdrawals processed from these sites. That's my own personal experience too, spending coins from a web service that ended up with a 400 sat/byte fee during the 300k mempool days. I accelerated that on antpool and it got confirmed in 2 days (estimator said 3 days), so I'm assuming it still works.
I've also now stopped accelerating for most people. I think a lot of us have been duped by newbie accounts feigning ignorance and asking for low-fee txs to be accelerated.
Theories about antpool: probably correct. They still accept valid tx IDs, so they must also have a queue that's virtually a mempool within a mempool. With its own (less severe) fee prioritisation.