This seems to presuppose that combat and roleplaying are at odds. There are a number of RPGs whose design is grounded in a denial of this presupposition - at least Burning Wheel, The Riddle of Steel, and 4e.I suspect in roleplay heavy games that combat balance didn't matter as much, but in combat heavy games the combat balance mattered more
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I wonder if this divide has any corrolate with people saying that you can't roleplay in 4e? I certainly don't believe that's true, but on the other hand, perhaps people that were roleplay heavy were more happy with imbalance in 3e? Those that were more combat heavy (I'm not sterotyping here, but I'm sorta drawing a mental venn diagram and classifying different sides of a scale) found that the balance of 4e really improved the game.
If the orientation of a game is that roleplaying, in that game, should be focused on combat; and, if a game treats combat as one of the most important sites of conflict; then the character and quality of its combat rules will make a signficant contribution to the games support of roleplaying. (Of course, how mechanical balance would factor into this is a further matter. But it's probably not going to be unimportant.)
The 15 minute adventuring day is not just about combat. As VB and others have indicated, it's also about the mid-to-high level wizard's dominance of non-combat (via Rope Trick, teleportation, etc).If combat is not a major focus of the game, then balanced combat doesn't really matter much.
If outside stuff is a major focus of the game, then having that be explored and interesting does matter quite a bit.
A system which gives the wizard less of that sort of control is, I think, less likely to see the 15 minute adventuring day.
This is probably extraneous to the general point under discussion, but I don't understand how or why enemies can't be tricked in 4e.They made combat better balanced (but perhaps less "nifty", e.g. illusions tricking enemies etc.).
Do you have any particular design in mind? Eg you could remove the wizard's ability to nova; or you could remove the wizard's control over the non-combat environment. Either would go some way to removing the systemic underpinnings of the 15-minute day (4e opts for both). Either is likely to be controversial in some quarters. But keeping (or reintroducing) either feature is also likely to be controversial (personally, for example, I have no real interest in going back to a game in which PCs can nova, both for balance reasons but more importantly for aesthetic reasons).What if 5e fixes both issues?!