Adding another exhaust mechanism would possibly ensure you don't miss out on campsite interactions, if you're beelining for the cure, but IMO they should accomplish this within the current exhaustion system. I mean you are already kinda forced to rest in order to memorize spells, heal, regain class skill uses etc. so why not just make it so, that you don't miss out on character interactions, even if you're just racing towards the cure with minimal amount of resting.
It however wouldn't make the sidequests not related to removing the tadpole seem any less problematic from the RP perspective. They'd still have that sense of wasting valuable time and/or eschewing RP for completionist approach to the game. Also, I don't recall, the druid patch version I've most recently played, and the first EA version, being very different in regards to framing the urgency of your PCs medical condition. Just that the "you have more time" -insight maybe got more underlined. Unless you're into "alternative reasoning", your predicament hasn't really become any less urgent.