I suspect that /day powers will be balanced because:
1. Not every power will be useful in every situation. For instance, an area-affect version of a normally single target spell is only going to be worth casting if you can get the bad guys to stand in formation. With combats only lasting 3-5 rounds, and with added mobility, this may be hard to do. Once it happens, BLAST THEM, but it wont happen every encounter.
2. Some /day powers will be overkill and wouldn't be wasted on some encounters. For instance, a single-target high-damage blast would be very useful attacking that Troll Brute, but would be wasted on any of the 6 orcs that attacked in the previous encounter... or the next encounter.
3. Characters will have enough /day abilities that they wont blow them all in the same encounter and feel "used up". Taking the first 2 points together, a wizard might uses his area-blast on the Orc encounter and the later on use his high-damage blast on the Troll. Assuming that either of these powers are enough to turn the tide of battle, the player wont feel the need to keep spamming similar powers on the same encounter, which means he/she should have some gusto left for later encounters.
If a DM decides to throw encounters together that are WAY about the group level, then that DM is encouraging his players to burn through as many /day powers as possible. Thus we are back to the 5 minute adventuring day, but it would be the DMs fault. If a player decided to blast every Orc with his /day powers (overkill be damned!), then the problem creeps back, but this time it's the players fault.... and the DM has a troll break down the door to their cozy room at the inn, screaming "that Column of Flame would be pretty handy now, WOULDN'T IT?!"