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It does sound a lot more palatable once you point out how it parallels ‘on purpose.’
I don’t feel as bad about ‘the floor needs swept’ if verbal- It’s obvious enough that it’s short for the other form (and there’s nothing illegal about shortening sentences.)
Now this is a weird thought: The whole history of any language must be a series of head-shakings and hand-wringings to new words and usages. How else can any language develop ?
My wife used to say “on accident”, which I, too, took to be a natural mistake extrapolated from “on purpose”. “By accident, on purpose”, I used to exhort. She’s now my ex-wife, I’m sorry to say—for other reasons, I’m assured.
When my family moved from Minneapolis to Pittsburgh, back in the late ’60s, we discovered the second construction kc mentions. The example I remember best is from high school, an obstreperous “Hey—you want punched?”. But it could take almost any form: the floor needs swept, the dog wants fed, the car needs fixed etc.
Some local oddities bother me; that one never did. I didn’t retain it when we moved on, as I will with some expressions (for example “y’all”), but I remember it with some fondness.