There wasn’t enough quests in early vanilla. Blizzard didn’t even intended to make quests the core exp source. They were meant to move players from zone to zone only (and farm mobs for exp)… but people liked quests so more and more were added. With late classic there is a good surplus of quests.
Also at 60 it’s worth doing all non-gray quests if feasible as they will give way more gold due to max level bonus. Good way to get at least few hundred gold.
Addons like Questie and/or ClassicCodex show markers on the map for you for available quests that aren’t necessarily in your direct path. Maybe an NPC in an inn in Stormwind sends you to collect something in Arathi, while an object you find (or the marker indicates where it is rather) in the world in Arathi sends you to Tanaris. Stuff like that were hard to remember or even know about but it all adds up.
Many zones also have quests that span from green to red in terms of level. Meaning you can do 5-6 quests only to have to move on to another zone and then return later. Addons also make this easier.
Players “not having enough quests” for that final strech to 60 most likely missed many of these, which was not uncommon at all. Without having a source to back this up, I also think that along the way there were added more quests (at least in the higher level zones) up until 1.12 than it was at launch
I skipped searing gorge and burning steppes while levelling. I also skipped most of Hillsbrad.
You can opt out of any zones you wish and just grind exp. I pretty much opted out of questing entirely at 54 and ran BRD until 58, then moved on to other dungeons.