The US sense came about from the sense of "I'm setting this on the table while we discuss other things". The meaning then evolved a bit of sarcasm with "while we do other things", starting to mean "forever". I do agree that the UK meaning makes more sense though.

As an American, I can't see the logic in having the relationship between a proposal (which is an idea that may be embodied in documentation) and a table (which is a thing that we rest our beer upon) as having any importance at all -- regardless of which way it goes.

It seems like plain speech could be used, but this profoundly-irrational jargon was selected instead.

I guess US `tabled` means put in a writing table drawer, hidden and soon to forgotten.