I'm not really concerned about those private keys when I use an exchange, because I never plan on keeping my coins there--and you're absolutely correct; nobody should be keeping significant amounts of crypto on any custodial exchange.  That's something every newcomer to crypto should learn, but unfortunately some of them have to learn the hard way.  There was just a thread the other day about some Asian exchange called FCoin that supposedly pulled an exit scam, and that's the big danger.

Also, I don't have a problem with those traditional, custodial exchanges as long as they're trustworthy, and some are.  Coinbase, Kraken, Binance, and a few others are regulated and probably aren't going to get away with exit scamming even if they were inclined to do so.  And even though I still wouldn't store my crypto on any of those, I would feel comfortable trading with them and leaving coins there perhaps overnight.

Noncustodial wallets are just stupid, and nobody should be using them.  That's another thing newbies need to learn early on.