You could either make an exception for funds, or simply make them owned directly. Probably impossible before computerisation but fairly straightforward now.

These don't seem difficult problems to me.

The difficult problem is how you distinguish a fund for consumers versus the types of funds you want to disallow. Start trying to codify that in law and it will quickly bring people finding the edges for their own purposes.

Full public disclosure of all beneficial ownership in entities would go a lot further, IMHO.