what are the downsides of voluntary taxation (https://en.wikipedia.org/wiki/Voluntary_taxation)? what would happen to a polity that used it as the sole form of capital allocation?

The only problem is externality pricing.

Building https://negationgame.com

this is the biggest downside i see. worth asking: would whatever “tragedies” that occurred in this system still be better than the alternatives we observe today with compulsory payments?

what about communities, who have skin in the game, acting in their own self interest?

we raise taxes to address externalities

so whatever you think private industry can't profitably address (public goods or public bads) you're gonna have problems