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is it better Wikipedia lack articles that humans can't or won't write?

Yes. As long as it's properly cited (not that many people look anyway) it's easier access to information. A starting point for further research.

Can robot-written articles be trusted?

No more or less than any other article. There are many reasons articles shouldn't be trusted, including paid editors, people with biased views, people with out of date information.. etc. You shouldn't take anything at face value, that's what citations and research are for.

Should they be labeled and approved?

Maybe the accounts should be labeled like payed editors are now supposed to be now. I don't see why they need more approval than a "real" person. If you find out a bot has reoccurring problems, ban it 'til it's fixed. Reverting and deleting isn't a major issue.

And lastly: is all this work even worth it in the first place? Do these bot-written articles even add any value to everyone's favorite information site?

The authors must believe it is worth it. You can't stop it. If people want to they will find a way to flood Wikipedia with whatever articles they want. By trying to limit them you will only inconvenience "real" users.