Why do we use pay top dollar and not pay top dollars? Dollar is countable, so dollars look more correct.
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I think the idiom started with advice by the State Board of Agriculture in New Hampshire, 1901...
Originally it didn't mean "obtain the top price" so much as "look to the 'margin' over fixed costs". Advice repeated in 1907 with similar wording by the equivalent Board in Massachusetts...
...and Vermont (but probably meaning, or at least implying, "top price" already)...
...then by 1911 in trade publication The Poultry Item (definitely "top price" by now)...
It's not until 1931 that I find the first instance of "pay top dollar" (with the article "the" discarded), and even then we're still in the farming context, with American cattle producer: Volume 49
Thus we see the dollar was perforce single when it started, and as the meaning gradually shifted, there was never a convenient point where it could be pluralised.
The phrase is often used in Britain too, but our own nearest "native equivalent" is pay top whack.
Imagine a stack of money. If you pay top dollar, you pay with that top dollar and every dollar bill under it in the stack. In other words, you pay a lot. It is an American idiom.
This idiom is also related to bet your bottom dollar. Same stack of money, but now you're so sure of something, you would bet it all from the top dollar down to the bottom dollar.