I think this is a horrible idea - at least if it was mandatory. A lot of the joy of the maps comes from gallivanting through them and exploring them. A lot of enjoyment of the story/stories - at least for me - comes from figuring out what is going on, not only with the tadpoles but with all the little side-stories. I don't need a timer that forces me to be more conservative with my spells - which would make combat less fun - and miss out on camp scenes so I can enjoy the maps while also keeping my bar from cluttering up with (illithid) spells I never use. For me Lae'zel never shutting up about the creche and the zaithi'sk is enough of a timer.
Because really, the above doesn't add a timer, it just forces you to long rest less. Which changes little for melee focused groups but is a pain if you prefer casters. It also contradicts the idea of the astral prism which keeps you safe from the effects of ceremorphosis.
I wouldn't mind more time sensitive maps though, I love the Iron Throne and think that it is an excellent example for what a timer is good for.