I suspect they would find some efficiently fraudulent manipulation in the complete absence of regulation, if only those exchanges were regulated enough to retain data sufficient for such inquiries.
Fortunately all the cryptocurrency in and out transactions are irrevocably documented on a public legder.
The blockchain doesn't (consistently) tell you who owns which wallets, nor if they're a terrorist financier or money launderer. This is besides the point that "exchange" has a specific legal meaning under the Securities Exchange Act of 1934, as amended.