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 they don't store any funds.
First we have to ask "why do governments regulate exchanges in first place?".
The answer is for a couple of reasons but the main one is to monitor people's financial transactions more. In simple terms: for more surveillance.
Now back to the quoted part, the government that wants to monitor how much money you have in a cryptocurrency and how much profit you make (to tax you) where your coins come from and where they go, etc. needs to enforce regulations (KYC and other restrictive measures) to gather information on you and monitor you better.