Most flights are padded, I constantly have pilots who announce "we managed to get you here a little ahead of schedule despite the delay" because they have an extra 45 minutes time in the flight schedule so a 30 minute delay doesn't result in a late arrival.

I would rather leave late than arrive late because I'll have business, people expecting me, or another plane to catch at my destination. In the case of some short turnarounds (eg. 30 minutes between flights), getting there 30 minutes late means waiting for the next plane with a seat -- which could be the next day in some cases.