It's simply false to say that mechanics are irrelevant to this.
I was speaking solely for DnD. A game like GURPS for example doesn't have a fifteen minute adventuring day because their system is completely different.
As far as DND goes, the mechanics are irrelevant. You can either allow the 15 minute adventuring day or take steps to elminate it as I have done.
The mechanics do not create the 15 minute adventuring day, the players do using metagame thinking to do so. So you must create encounters that discourage that type of metagame thinking.
That means running encounters so that it is advantageous for the party to continue fighting because if they don't the BBEG will have time to regroup and retaliate.
In my experience most players want to play, not watch.
I've already come to the conclusion that I differ from most players. I always liked the image of being the wizard who turns the tide of a losing battle. I didn't mind waiting until I was needed.
I understand that not everyone likes to play the low key wizards that unleashes his power at key moments.
I'll tell you how I solved the 15 minute adventuring day a a DM.
I lumped my encounters together. I generally ran modules with a large focus on some BBEG or long adventure arc.
I would break the arc down into a series of events. Each event was a long battle meant to last quite a few hours which I glossed over with roleplaying. Rather than spread my monsters out to be killed individually, I packed the monsters together and had them make war like an organized, intelligent force never letting the PCs rest unless they earned that rest by killing their enemies and holding their ground.
For example, in the module
City of the Spider Queen the party was forced to fight a non-stop battle against the entire compound once they attacked the first guard post. The vampire leaders of the compound did not sit static and wait for the party to arrive to kill them. Instead the alert was sounded and the entire compound descended to try to kill the the party and the fight wasn't over until they squared off and finished enough of the forces to force the vampire leader to her coffin.
I do this with almost ever module I can. I don't leave monsters standing around in their room waiting to be killed unless it is an exploration adventure with random, ruined rooms. But coordinated areas of humanoids and the like go on alert and start what I refer to as domino encounters: large-scale encounters that set off as a series of events.
That is how I used encounter design to elminate the 15 minute adventuring day. If the mage or priest was foolish enough to blow off all their spells in one big burst, the party was most likely going to die.
It may not be a fun way to run for all people, but my players got very good at resource conservation to the point where they still practice it in 4E. They fear to let off dailies because they are never sure when they are going to get a break.
I'm glad myself and my players were forced to play this way. It elminates cheesiness like the 15 minute adventuring day and forces them to think like a soldier might think with limited ammunition when he is at war. The luxury of unlimited resources due to the 15 minute adventuring day was something I will not tolerate from my players.
It ruins my view of what an epic encounter should be like. As far as I'm concerned an epic encounter should require a coordinated effort by the party that leaves them feeling exhausted, spent, and like they just barely escaped death to achive victory.
I didn't feel that following the standard module design of compartmentalized encounters allowing for the 15 minute adventuring day created the epic feel I wanted in my campaigns. So I ran it a much different way.
That's how I elminated the 15 minute adventuring day. It's not everyone's cup of a tea. But since people enjoy playing in games I run, I'm going to keep running it the way I like to run it.
If some people don't mind the 15 minute adventuring day, they can use the compartmentalized encounter system found in most modules just as they are written. It encourages the type of play that leads to a 15 minute adventuring day.