I've had the 20 minute day in my groups, and I'm a pushover as a DM. I never kill characters except for 1 TPK in a 4E game simply due to the dice. In my games the 20 minute day comes from the deep immersion style we play in. The players are genuinely worried about what is in that cave, but as long as it isn't coming out and doesn't have reinforcements, they do the logical thing. It isn't, however, the best for fun or story.
But realistically, especially if facing an intelligent opponent, a 15 minute adventuring day just gives your enemy time to outmanouever and out gun you. It's a losing strategy if you're playing realistically. The enemy gathers his strength and either throws everything at you while you rest or in the first area you return to, or simply ups sticks and leaves the area.
In any kind of dynamic, consequence based game, stopping doing everything after 15 minutes (which also implies that your magic users simply use their magic constantly, without husbanding their resources for when it's most needed), is an invitation to utter defeat.