It doesn't make the fire die faster, it just passes time faster.

That said, I do think melting/boiling should be combined into the same action that takes longer. Even on Interloper, I've never once died from being forced to drink unsafe water that I couldn't boil for some reason, and it serves no real game purpose. Unsafe water feels like a leftover from an early build of the game, it's just busywork now.