The reason for this is because GPS's rely on their last known position to help speed up the fix. They also use a database that is updated regularly to help predict where the satelites are going to be.
Good point. The eTrex I have can take 15 minutes (worst case scenario) to find a fix. So, yes, that's a reason to take it out of the bag and switch it on quite early. If it's been used recently and I haven't moved a significant distance since then, it'll normally get a fix in two-three minutes though.
That particular eTrex is over ten years old though. Modern units with newer receivers should be a lot quicker. On the other hand, I've used it so often for all kinds of purposes that I do know how to use it to the fullest extent. (Admittedly, not that hard with only five buttons and five main pages.)