I can't say in terms of classic, but it's really not that unusual a thing in bfa.
Let's take a "balanced" mythic raid (no class stacking):
3 plate
4 mail
6 leather
6 cloth
19 total
You pay to get your Demon Hunter (was gonna do Druid, but you'd probably call that extreme since they cover all roles and would get more loot because of it) boosted and you get all usable items. That means:
All Leather, Rings, Melee/Tank Trinkets, Most 1h Weapons; Chance of a player getting an item is slightly higher than 20% (since personal loot provides a small bonus over other loot rules, afaik they didn't remove that since I regularly see more than 5 items in a 20 man raid and very rarely less than 5).
6 leather users with ~20% chance of useful drop (leather, rings, some trinkets, some weapons) = 1.2 drops per boss
3 plate users with ~12% chance of useful drop (rings, all trinkets, many weapons) = 0.36 drops per boss
4 mail users with ~8% chance of useful drop (rings, few trinkets, few weapons) = 0.28 drops per boss
6 cloth users with ~5% chance of useful drop (rings) = 0.3 drops per boss
your personal loot with ~21% chance of useful drop (21% is aiming low) = 0.21 drops per boss
Total of ~2.35 drops per boss
We'll say 10 bosses and that's 23.5. That qualifies as "dozens" from the original
quote.
The 60 claim is high, but doable in a heroic boost because you can both get 30 players into the raid vs 20 as well as making it significantly easier to stack by armor type (with 10 bosses, all leather raid would average over 60) .
I think the more salient point might be that in
retail you can probably get gear for almost every slot in a single run. Remember, there's only 15-16 slots and right now 2 of them are reserved (artifact necklace and legendary cloak). When I was Mythic raiding in Legion my guild was nice enough to carry my freshly dinged alt through heroic Antorus and by the end of the run I had gotten an item for all but one slot (bracers I think).
In classic this is significantly less likely because there's far less drops (and for some classes/specs, less USEFUL drops).