Because everyone will have this currency by default, natural market forces will causes businesses to want to sell things in that currency (people have it, and want to spend it).

The currency itself is stable (tied to GPD growth, not politician's whims).

Once some businesses decide to take it (and they will, see above), then those businesses getting that income will also spend it at other businesses who accept that income, making those businesses even more successful, causing other business to also accept the currency, and so on.

And remember: everyone has some of this currency. Who is going to have it, and not spend it? I'd venture to say the percent of people flushing their basic income down the toilet is in the low single digits at best.

It's a virtuous cycle, and no force should be needed to keep it going. Think about it: who in their right mind would move to another currency that wiped out their entire existing and future wealth? As another commenter pointed out, $11K a year is like having $500K in wealth paying out an annuity. Who would voluntarily give that up for some alternate currency that makes them poor?

Even today, look at how hard it is to modify a social welfare scheme. It's not because the government has guns and the desire to use them, it's because people really, really rely on social stability.

But yes, you're right of course: like all fiat money schemes, it only works because people want it to work. IMO people will want this to work, and furthermore: it's in each individual person's self-interest that it works.