As someone who runs every day and does a few long distant runs every two weeks, I wouldn't really want anyone having my underwear. Even though I wear sports underwear or sports clothing with built in underwear, it still get pretty rank after a run. TBH after running 13.1 or 26.2 miles I almost considered replacing the clothing, but that would be too much money for me. So it goes into the wash asap. I don't really see why it would be nice, my OH doesn't seem to like my body smell after a long distant run, and if I don't wash striaght away you get a dried salt texture on your skin and clothing. I think shorter distances, the smell wouldn't be so bad, maybe even nice.
I should be running 13.1 mile today but in two runs, so will end up changing my running clothing twice and washing twice. But one 5mile run and one 8mile run doesn't often make my body dripping with sweat like a full 13.1 or 26.2... tend to find that around 18-22 miles is when my body really starts to show it's getting tired and sweating loads.