What a lovely metaphor this is. So evocative! Everything about it is clear, except perhaps: why would you be holding a hot potato to begin with? Well, that's life, sometimes someone hands you a hot potato, or one drops into your lap, and then there is nothing to do but get rid of it again, as quickly as possible.
For metaphors, I like thinking about what a non-native speaker would think of them. Good metaphors stick with you. When I was studying Korean, my teacher mentioned the simile “flat as a squid”. I was confused. “Flat as a squid?” I asked. We confirmed that we were both thinking the same for “squid”, and I asked “why is a squid flat?”
But then the answer: the Korean phrase is alluding to a dried, pressed squid, which is a common bar snack. Aha! “Flat as a squid,” indeed. And I have never forgotten it; if anyone ever said “flat as a squid” I would think of the dried squid again.
I think “hot potato” is like that. Maybe the Koreans don't say “hot potato” but they do have potatoes and it's immediately obvious that to drop something like a hot potato does not mean to drop it grudgingly and reluctantly. I don't know if Koreans ever say anything like “flat as a pancake” but they do have pancakes of many sorts and I'm sure they would understand right away.
I tried to find out: does the phrase predate the game of Hot Potato, or did the phrase come after and specifically allude to the game? But none of the usual dictionaries was helpful.
[ 20171120: The answer ]