Implementing a mechanic like this in the very tutorial level would probably send the wrong message: "DO NOT STOP EXPLORING!!! HURRY!!!"
"You stopped to help this woman stuck in the pod? Now you made things harder for yourself!"
The game already creates a false and unnecessary sense of urgency with the tadpole storyline. Some people are even skipping long rests to avoid being turned into mindflayers when an invisible timer reaches a limit. There is no need to create such stressful measures. Why not let players explore things at their own preferred pace? The only reason I was more chill about it, because I've already played a few dozen games that start with "Hurry, the apocalypse is imminent!!!", but you actually have all the time in the world to play some cards in the local tavern.
