This is far from a new idea, it's coming from the banking sector, and I believe it should suit cryptos exchanges just fine. Because there are 2 kinds of exchange.

A normal exchange is a company which exchanges fiat currency with cryptocurrency, and vice-versa, taking a small fee in the process. And that's it. Nothing else. I believe these exchanges hardly need to be regulated, because most often they don't store any funds. You make a deal with them, and when it's over, the customer relation is over, everything's terminated.

Besides that, there are exchanges which offer margin trading, which propose lending and borrowing cryptos, and various other high risk activities. Those exchanges need strong regulations, to protect investors.

We have about the same differences between commercial banking and investment banking, and there are many economists arguing about the need to separate (or unite) these 2 activities. We shall have the same discussion with cryptos exchanges.
Many legislators around the world are talking about regulating exchanges, this is what they should talk about first.