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.
I think the names in the original post are a bit confusing, though, which is probably why many people won't get the difference right. I think I got it right, but only because I have experience with both types of platforms.