>where paying out a lot of basic income one year results in fewer taxes the next year, which means the government has less money to pay out in basic income that year, causing people to need to a job, which increases taxes the next year, after which the government can pay out more in basic income.

There are problems that need to be solved, but the one you have here you just invented. Government programs don't work like this. They aren't pegged to revenue.

The problem you described with oscillations and feedback loops is exactly one of the primary criticisms of attempts at forcing the government to balance the budget each year.