The suggestion in my OP does not remove resource management. It adds an additional restriction as to how those resources are deployed. To use your SpecOps example, the sniper can carry around dozens of bullets, but he can't fit them all into the same magazine.
First, none of this would change for your group with the rule I've suggested. The wizard would still only have X spells per day, chosen in advance; he just wouldn't be able to use them all in one encounter.
Second, (and here's the part that makes this debate frustrating for me), I think a game with balance between character classes actually contributes to teamwork and clever tactics. If the wizard's burst potential is more limited, it forces both him and the rest of the group to play closer attention to tactical considerations. Let's take, as an example, a 5rd-level wizard who can cast 4 first-level, 4 second-level, and 3 third-level spells per day. Let's say under my system he can cast 4 spells in an encounter. Early in the morning, the party encounters a fairly large band of roaming orcs. In both versions, the wizard knows that this is only the first encounter of the day and he shouldn't blow all his spells on it. But in my version, he's got an extra consideration: if he uses all his first-level spells and the orcs prove more dangerous than expected, he can't just toss out a fireball to clear the room, so maybe he should use a higher-level spell early instead. And if the group DOES decide to save their powder on this fight, then they'd better be ready to keep the wizard protected, because he can't just blow all his spells to save the day if things go wrong.
Third, even if my first two points didn't apply, your group isn't the only one playing D&D, and the core rules should accomodate the "combat as sport" folks WHEN it can do so without messing things up for "combat as war." Now, if I were suggesting 4e-style wizards with predominantly encounter powers, you could justifiably complain that I was messing up your fun. But since (as far as I can see) all I'm doing is enforcing a resource-management approach your party is probably taking 90% of the time anyway (how often would your wizard blow more than 4 spells on that group of wandering orcs?) this might be a case where the game could be adjusted to better suit both Bob's party of medieval gladiators and your SpecOps murder hoboes