One quick drawback to your proposal — What prevents a state/city/town from firing their existing work staff and hiring these unpaid “volunteers” (for lack of a better term) to replace them?
A whole lot of municipal employees would get laid off (all losing perfectly good paying jobs, pensions, health care benefits, etc..), states/cities/towns would slash their operating budgets and the Federal government (who would presumably run your proposed program) is left to pay these people their increased UBI year after year.
The same thing would happen with those “public/private partnerships”. If my State wanted to rebuild an interstate highway, the selected contractor only hires a skeleton crew of professionals to run the show and then everyone else are unpaid workers. Concrete workers who were getting paid $60k/year would all be out of work in favor of unpaid workers.
Essentially, any government job that doesn’t require very specialized skills would go away. There are ~20 million people that work for government entities at one level or another. Your proposal would probably replace 90% of them with unpaid workers. Millions more would lose jobs working for government contractors, non-profits, etc…
So tens of millions of people would lose their jobs and any benefits that go with those jobs and, because they would no longer be working, they also wouldn’t be paying taxes to fund your proposal.