Even Greener Pastures

Further question: is it wrong to say thuh onion, thuh elevator?

No, it isn't. However, you'd have to introduce a glottal stop* between the article and the vowel, otherwise you'd end up saying "thonion" and "thelevator", and that, I think, really would hinder understanding.

*a glottal stop is that kind of slight gagging (where your throat closes up for a moment) which occurs at the beginning of ejecting a very short (surprised?) "uh", or try to pronounce an exaggerated "g"

This is from the Oxford dictionaries:

Note how he says "it's not impossible", implying it's not really common.