15-minute adventuring day is merely the label. What is really at stake is, "are the players attempting rest more often than the preferred style of the current group would indicate, out of a desire for more power concentrated at the sticking points and/or insufficient challenge?"
How about this as a related tangent? As a general design principle, when a DM makes his adventure, out of "encounters" or "monsters" or "rooms" or "areas" or whatever, this should be something that the DM uses as a tool--but not transparent in the result to the players.
So say we have a starting party adventure, a typical cave complex heavily populated with kobolds or goblins, a few traps, an oddball monster or three, a witch doctor, and some nasty monster more suitable for characters a couple of levels higher. (We'll assume we have decent background, situation, proto-plot, etc. to make this non-generic and suitable for the gaming style, but it isn't relevant to the point.)
Now, there are some interesting locations in this complex. And if things go more or less as expected, some of the bigger fights will happen in these spots, at least part of the time. You might get some "running" fights that go through such areas. And we'll also assume that there is far more in here than a starting party can handle--certainly not without some rest. They are expected to retreat and/or hole up two to three times before clearing out the whole complex--or perhaps hit it hard a time or two, then go do something else before they tangle with the tougher parts (i.e. gain another level elsewhere).
So far, whether you have a 15-minute adventuring day will depend upon the DM making this place come alive (i.e. not allowing camping in a heavily traveled hall) or the players avoiding such a style (whether out of native caution, heroic characterization, or simply wanting to get on with it).
But the main point is to kill most of those monsters and take their treasures, thus gaining power. So the characters are going to attempt to divide and conquer as much as possible within the confines of their preferred style--including extra resting for repeat use of big guns. And the DM will attempt to thwart that, again within the confines of the preferred style.
Certainly, if the complex is static, and the "encounter" design is transparent, it will take an act of will even for players who want to "get on with it" to risk their characters when a rest is almost assuredly safe. OTOH, if the place has monsters moving around and reacting to what is happening, then safety is tenuous. At that point, it only becomes necessary for the DM to create a perception of risk/reward being uncertain, to encourage the players to stick to the preferred style.
So if I'm correct in all that, it seems to me that the edition-spanning answer (i.e. that would work, not what is encouraged or in the RAW of all editions) would be to go to an all quest and/or treasure-based XP system. No XP for monsters whatsoever. Then a DM always has an incentive to include more monsters than are necessary, but spread them out. If the PCs camp in the main hall, they get several groups of weaker monsters at once,
gaining nothing in the process. OTOH, one would assume that giving the numbers of monsters, this will happen at least a few times even with clever play, thus producing the exciting battles.
After all, it is true that the LotR characters rarely fought 4+ encounters in a day. But when they went through Moria, they weren't looking to fight, and had a lot more than 4+ opportunities a day for a fight.
