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?

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

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

This image does a good job https://i.imgur.com/n9Pcbcr.png

not sure i follow. source with more context?

It's a bit hard to convey. Essentially, tragedy of the commons is the biggest downside because it's the only downside. Voluntary taxation isn't taxation, it's investment, people do it because they want the upside and because the upside accrues uniquely to them