Perhaps the free government accounts could be exempted from that red tape, and be capped to a maximum turnover amount such that it isn't attractive to money launderers. Once your turnover exceeds that cap, you have to "upgrade" to a regular account with all the KYC stuff.
Yep, that'd be the solution. The issue comes with the fact that these regulations are based on the "guidelines" set by FATF - which is a political organization and they make really idiotic decisions.
To some extent I believe the larger financial institutions lobby for these regulations in order for them to not have to serve low income customers.