Nothing about downloading an MP3 that says they can't put a targeted ad in it; there's podcasts that do that based on your IP. I assume the reason most don't is just how much more trustworthy it sounds when the host reads an ad script live in the episode.
(I swear there was an episode of The Weeds where they read an ad for a therapy service for dogs.)
(I swear there was an episode of The Weeds where they read an ad for a therapy service for dogs.)