There's a moment when it can add tension. You find three silver arrows in an old fort, hole up for the night, and then hear the horrible howl of a werewolf ring out.

Or you're lost in the desert, trying to ration your water until you can find an oasis.

I've played Westmarches games where you do a little pre-adventure "we need to go X hexes so we're wanting Y supplies to get there and back". But its more a cost of failure than a drama element.