1. Self custody is hard. You need to understand how to setup a wallet. If you lose the keys to that wallet, your money is gone. Opening an account on an exchange is so much easier, and there is usually a way to reset your password if you forget it.
Exchanges provide an online-banking style experience that most people are already familiar and comfortable with.
2. Access to markets. If you hold funds somewhere else, it takes quite a bit of time and effort to move it back onto the exchange so you can sell it later. It only really works for people who want to buy some coins and stuff them under their mattress until later. For anyone who wants to play the markets, you kind of need to keep your coins on the exchange.
Additionally, holding coins on the exchange is free. You don't have to pay the transaction fees to withdraw and deposit, which can add up, especially on congested blockchains like bitcoin and ethereum.
Non-KYC exchanges outside the US and sharp deranged claws of the FTC and DoJ typically depend on exchange held crypto if you want near instant clearing for futures and securities trading etc.
I mean, like, take, say you get out college or whatever you're doing. You're gonna go into business; say you're going to open a bank. Now you, just for example, you've got to give it the right name. It's got to be something big and strong like Security First Trust and Federal Reserve. And you have to name a bank that because nobody is going to put their money in Fred's Bank. "Hi, I'm Fred. I have a bank. You got $1,500? I'll put it, I'll put it here, in my white suit. White suit, right-hand pocket. Ok, you gotta remember that."
(you probably have to listen to get all of it)
If you don't trust that seed phrases, which are a fundamental piece of how bitcoin key pairs are designed, will work why would you ever consider investing in bitcoin?
I totally get the stress of self custody. I just don't get why anyone that stressed about it would bother buying bitcoin.
During the Terra collapse, there was a 2-day period where Terra's price was supported by a massive BTC reserve. Those with Luna on exchanges could quickly exit their positions, but those with Luna in wallets or locked in Anchor Protocol faced hours-long delays for their currency to be confirmed and traded.
Binance in particular has its own blockchain and gets to run fractional reserve on most of the assets bridged to that block chain - the bridge keeps the real copies of the assets while only "shadow copies" are "projected" onto the Binance chain and traded.