"On the clock" should exist as a story pressure first, and as a social pressure only distantly second, IMO. The point is to rationalize there being a short amount of time to make decisions in character, and then to use that pressure to keep things from stalling out around typical time-wasters such as the "shopping trip" or the "session long no-actual-plan-coming-out-of-it planning session". In the DFverse, it's also important simply because some problems can be solved with thaumaturgy + enough time. But when does Harry have enough time? (Granted, thaumaturgy needs the right material components in order to be possible too, so that's as much of a limiter as anything. No blood/hair from the bad-guy, there's only so much you can do no matter the amount of time, etc.)