Given that the assumption is typically that each opponent begins battle with no damage and all his limited-use abilities available, one could argue this is actually fair: strength against strength.
It might make casters somewhat advantaged at high levels, but again, I find the chances of a 15th level character fighting two challenging battles in one day fairly slim. How many monsters that powerful are there in the world?
In any case, per day limitations are never going to balance casters with noncasters, so changing those limitations doesn't fundamentally change the balance of the game. The problem is that casters' spells are just too good and fighters don't get enough abilities (problems that various 3.5 derivative such as TB & PF have attempted to address). In TB, a fighter actually has extra minor actions available per round; becayse what you can do in a round is a much more important balancing factor than what you can do in a day.
Balancing things based on actions (economy of actions) is a really nice way of thinking about power levels (and makes the issues with monsters intended to challenge a party by themselves a lot more clear as a design goal). I agree that casters and non-casters are not balanced, as is, but I am concerned that the 15 minute rest period will accentuate these differences rather than minimize them.
In AD&D the trick was to make memorizing spells very lengthy and to make sure that there were no "risk free" ways to implement the 15 minute adventuring day (teleport being the modern example).
I suspect that focusing on these elements might be more productive . . .