Good for you for finding what works for your group. I think any given group can find house rules to fit their style. I am taking the thread topic to cover more addressing the situation overall/across the breadth of gamers.
As an example of one where a time constraint is hard, I would suggest 'let's go explore that long-abandoned _____.'
I'm not sure I find that hard, though. If exploration takes time (like @iserith's 10 minute turns to explore a set area) and you have random encounter checks at regular intervals, or use a tension pool of dice, the time constraint is there.