Additionally, I wonder if basic income can be effective while there are still shitty jobs. Right now, somebody has to clean the toilets, because there aren't yet robots that can do it cheaply enough.

If you introduce basic income so that nobody has to do the shitty job, nobody will do it.

But one day there will be robots that can clean the toilets, and then there will be no shitty jobs left to do - and perhaps only then can basic income take hold.