So, one thing that puzzles me is why is the Pre-War dollar worth anything in the Post-War world where barter, gun and bottle caps are considered the currency of choice?

The only logical reason I could see buying Pre-War paper is the possibility of it being used as toilet paper or a Pre-War enthusiast. Anyone else?

I don't think it's a currency, but rather, a collector's item. However, there might be a town or settlement where it is still the preferred currency.

It's pretty damn under-valued.

10 caps for a stack of pre-war bills.

Probably Toilet paper.