There are many possibilities.
Many vanilla instances were very long; Mara, UBRS, LBRS, BRS, etc.; the physical size of the instance meant that it would take a while. This makes wipes even more time-consuming and has a multiplier effect on the time lost to respawns since longer runs mean more time for respawns.
Numbers: Did vanilla instances have higher trash than BC and WotLK instances? At first though of places like WC or BRD seem like trash-infested wastelands compared to a low-trash instance like... um... there's still a ton of trash. Think of ramparts and how much trash there is until the first boss or utgarde keep. There are the extremes of a 99% trash instance like SM armory/library (pull really fast or there will be multiple groups respawned by the end), which somehow people seemed to forget when praising SM or the extremely low trash of AN. Overall I don't see much change in trash from vanilla to BC, though a noticeable average decrease in WotLK.
Difficulty: If trash is hard, it will take longer. This could mean having to pull carefully, waiting on pats adding even more time. Or spending time figuring a kill order and maybe even CC. Sometimes I found vanilla trash harder than the bosses with lots of runners, enrages, fears, mana burns, spam summoning, and just plain high damage abilities. Scholomance had some particularly painful trash with everything from mobs that went immune to magic to zombies that exploded; and then there were the green clouds; hint: don't stand in them. This wasn't the sort of stuff that you just pulled and laughed off with a bunch of AoE, because it would have already AoEd down YOU. But much of difficulty is relative, gear changes it.
Relative gear: We're better geared than in vanilla. We don't run heroics (5-man Scholo pre-nerf or a Baron 45 run were the equivalents) in greens. We go in blues, even epics. That's to start. After a handful we're in half epics and unless we're doing some of the stranger achievements, everything is trivial. This is how tanks can survive AoE tanking and healers can survive healing that much damage. Gear is better itemized too; so we don't have shamans needing OOC spirit regen after 15 seconds of casting.
Class capability: On the subject of AoE tanking, there weren't any in vanilla. Warriors could tab-sunder and hold a handful off of healing, but may the Light have mercy on the mage who tried arcane explosion on anything that wasn't a trivial leveling instance or already fleeing from low health. We didn't need AoE tanking anyway because we didn't have a ton of AoE damage anyway (don't pretend I said we had none, I am well aware of the AoE requirements of Gluth, and the expected impossibility after the AoE cap); no seed of corruption or critting blizzard or bladestorm or fire totems that weren't bitten by critters the second they were dropped.
Trash definitely took longer, not because there was more, but because it wasn't so trivial. It was much more difficult in equivalent gear and it was much harder to outgear it. If someone did outgear it... well let's get to the next part.
Think of this as outgearing to the extreme. Someone who could not possibly need the gear drops runs the instance. This didn't happen too much in vanilla. If you didn't need the drops, you didn't go. There weren't badges or rep grinds to attract the overgeared raiders or to help overgear the rest. There were exceptions like live side Stratholme (for the righteous orbs, which were serious business), but in general people stuck to the content designed for their gear. There was powerleveling, but that was leveling. You didn't get run through a max-level instance like you can these days.
I won't try to speculate on this since I'm likely to slip into some haze of rose-colored elitist longing for the good old days when people worked hard and entrepreneurs would build bootstrap factories and we'd work there for 20 hour days until after a year we'd save up to buy a pair of bootstraps by which to pull ourselves up and dammit I never say an epic, but I did once hear a rumor of one from someone who'd run Scholomance 50 times in a row for a total of 200 consecutive hours awake and gotten an epic staff which was then ninjaed by a warrior who needed the int buff to level his weapon skills.
What I meant to say was: "Are players more or less patient with long instances, wipes, reclears, etc. than in the past?"
As Gnomegeddan points out, it's all about the loot. We want fast instances for loot, but might we also want slower instances for the feel of the world? Surely we desire something more than temporary virtual pixels.
FFXIV: Just call me Healbot 3000
11 hours ago