I don't think that they meant for you to be completely out of resources at the end of any given day. But honestly, I've never had more than a couple of combat encounters in a day and they PCs have often been down to their dregs. It seems balanced to me and the players seem to enjoy it.
An action casting a high level slot on average does more then an action doing an at-will action. If all we have are those, then the classes with the high level slots (and low level slots for utility and defense) will do more than the at-will characters. There's no question about intent "did then mean for you to be completely out of resources", it's entirely math. If you sum a bunch of numbers between 10 and 15, and sum together the same number of 8s, the 10-20s will be higher. It's not until you start adding in the 4s to the top list (having to use cantrips either to conserve slots or because you are out of slots) while the other list is still averaging in 8s, that they start to converge. The measure of that balance is the average efficiency of an action.
For the balance between classes to work out, the
average efficiency of an action must balance out by the end of the day. Now, not everyday - some days will (and properly!) favor one side or the other. But if it only favors one side, that's not balanced. And over a statistically approprite longer period, it should balance out if you want the classes to be balanced.
As a side note, I play with several DMs who don't do a lot of encoutners per day. It's definitely fun. But we've wandered away from the at-will classes. We have paladins and barbarians - both whom are hybrids that benefit from short days - and casters.
One DM also doesn't like giving short rests once the action has started - feels it destroys tension and pacing. We don't see monks or warlocks with that DM. Same general reason, about the efficiency of actions being too much lower than the average replacement. (WAR for you sabermetrics folks.)
Don't forget that longer combats mean a greater risk of losing concentration on spells or having enemies save against the effects, since most allow a new save at the end of every turn now. If you have casters, the enemies can see them and should be targeting them.
I won't forget, but it's meaningless. If a spell using a slot X and an action to cast is held for all of a 3 round combat, or is lost in the 4th round of a 8 round combat, there can be no argument that because it was lost in the second cast that it was the less efficient use of the spell. Enemies will be targetting regardless. If it lasts 3 rounds, it lasts 3 rounds. If it has the opportunity to last longer but doesn't, doesn't suddenly make it worse then the one that lasted the entire 3 round combat - neither is useful round 4 onward.