I usually use the first kind of exchanges, to be honest, as I don't need to store money on any centralized services and only transfer it when selling for fiat. There are still some risks here, as you can't be sure the exchange will follow through on their part, so some regulations are needed. But I agree with the op that the regulations should be harsher for those exchanges that hold the money of their clients, might use it for their own purposes (like FTX), and offer more services.
Regulations will become harsher certainly but if you use decentralized exchanges and store your coins in your wallets (non custodial), you will not have risk to lose your coins. In contrast, if you use centralized exchanges, you will have such risk and even bigger risk to lose your coins by harsher regulations that can cause drop in exchange trading volume, income, profit and might trigger collapses of bad centralized exchanges.
FTX is a very painful example of unbelievable terrible collapse of a Tier 1 centralized exchange. I did not think it can happen but after all with more information about their bad operations, their collapse makes sense.