One of the lost arts of old school D&D is that of waiting.
Consider the 1st-level wizard, with his one sleep per day. In most combats which aren't going horribly wrong, if he can't think of something clever to do, he waits.
Consider the everyone else while the thief is scouting ahead for traps. If they cannot think of something clever to do, he waits. They could risk HP and possible death by scouting ahead personally, but that's hazardous and not really in the party's best interests.
Consider the front-line fighter in a combat against undead, where the cleric is winning via turning, or where an oil wall is up. He doesn't charge in, though he might want to; instead, he waits and advances only when it is opportune, when risks have been mitigated and enemies weakened, or switches to a ranged weapon, or comes up with something else clever to do.
Consider the thief in a combat where the party has formed the Dungeon Phalanx in a hallway against a group of powerful foes. He waits in the rear and harasses the enemy with arrows or thrown fire, because even though his class abilities and his player's desire would have him in the enemy rear, he's very liable to be killed there, and that would weaken the party as a whole.
There's a lot of waiting and going "This one is yours to win. I'll support as needed, but really it's all you, buddy," to someone else at the table. This is a result of individual classes being able to win certain encounters or types of encounters single-handedly, combined with permanent deleterious consequences for taking unnecessary risks (PC death, level drain, TPK, ...).
Are there times in new-school games when an obstacle is one character's to overcome while everyone else relaxes? Sure. The canonical example is waiting for the thief working on traps, and it comes up with wizards solving wizard-puzzles sometimes. But this is often seen as poor form, for any player to be sitting idly for any significant length of time while someone else has the spotlight. One need look no further than the forum posts about how someone feels useless in certain types of combats to realize that this is not a solved problem in the new school.
They've made some attempts, though. Arguably skills exist to circumvent the "unless you can think of something clever" clause. The alterations to the resource expenditure paradigm in late 3e and 4e are designed so that casters no longer need to wait and choose their time to strike. The skill challenges system is designed so that everyone can participate in non-combat encounters, even if it sometimes mandates that they do so in nonsensical ways. The idealized combat-as-sport combat is characterized by each PC playing to his strengths concurrently in a single encounter.
It's teamwork, but of a different sort than that present in the TSR Waiting Game. If a combat in the new school is easy, players compete to do the most damage or kill the most enemies or land the killing blow, and those who perform poorly get sad at their lack of effectiveness. If a combat in the new school is difficult, underperformers are the recipients of blame and frustration at their ineffectiveness. In both cases, social pressures exist towards optimization.
Contrast with the old school. If you're up against undead, and you're a cleric, your stats don't matter. Your build doesn't matter. All that matters is that you're the guy who can turn undead and oh god please save us from these wights. We have a problem, you have the solution, and right now that's all anyone cares about. We're outnumbered 3:1 by orcs and you've got the sleep. There's a trapped corridor that we've already lost a henchman to and you've got the thieves' tools. And so forth.
The exception, of course, is the fighter. The fighter rarely waits; he's involved in most combats to some degree, being the tip of the spear and the shield of the squishies, but only ever gets the spotlight by default, when nobody else is using it - when the combat isn't serious enough to warrant arcane intervention, when it isn't undead, and after the thieves have already done their tradecraft (exception - single combat against enemy leaders. But that's fairly rare).
And I think that's why my group likes fighters in ACKS so much. Not just because plate and d8 HP make for wonderful survivability, but because they don't usually have to wait. The mechanics of the fighter most closely approximate those of new-school combat, among all of the ACKS classes, and so the play experience is familiar to my players, and they seem to enjoy it.