The point of a basic income is to ensure everyone has the means to improve their standing, and keep from sliding into abject poverty. Any use of the funds that furthers that goal is legitimate. Social pressure can be exerted to limit frivolous uses, but it's easy for that to go too far and become counterproductive.

The worst that happens is someone has more than they need. And then what happens?

One of two things:

1: It sits in the bank, where it's lent out for investment

2: It's spent, possibly on something optional but still legitimately useful and non-frivolous, in which case it flows back out into the economy

I don't see a bad outcome. The vast majority of people want to have the self-esteem boost of fulfilling employment, and will seek it out once they're not stuck in the welfare trap. There's even a solid chance this will bring civilization to a point where no one needs a minimum income.