It doesn't matter whether the overwhelming majority of people would be willing to clean toilets for however much money: what matters is whether enough people would that the toilets get cleaned. From what I can tell, the answer to that is "yes".

Given instructions, and absent other immediate obligations, I would do so much helping out, wherever I happened to be at the time. (The only reason I don't now is because I don't understand most jobs – my meddling could do more harm than good –, and they won't let me do jobs in my area of expertise.) I'm not unusual in this regard: perhaps I'm unusual in that I'll do this unprompted, but if it's a societal expectation that people clean up after themselves, and leave things in a slightly better state than they found them, people generally do it.

The problem is not a lack of workers. The problem is not a lack of things that need doing. The problem is a lack of "jobs". UBI (with the necessary patches to, e.g., prevent bad actors from redirecting all the money) is essentially employing everybody to do what they believe needs doing.

So the question becomes: do you believe direct democracy works at small scales? Your answer appears to be "no".