Purpose, probably useful, sure, I however do not understand why purpose seems to equal payed labour to you (and lots of other people). Are you suggesting voluntary work, or just being social to your neighbor has no purpose? I use these examples, because it is not certain that people even have the capability to always find "more meaningful" work if the "repetitive menial" labour has been automated. And why stop there? I suggest we are entirely capable of automating even "more meaningful" work. And then what?
Figuring our what purpose people have, if they do not need to work for basic Income, is one of the goals of experimenting with it.