The reason everyone loves Vanilla WoW: Nostalgia.
Want to tank? Roll Warrior.
Need gold for lots of respecs? Good luck.
AQ40 is current content and you've never raided? No need for you, impossible to gear for it.
Want to play a mage? Learn how to press frostbolt over and over again with the occasional blizzard.
Need to find a group? Spend hours asking in trade chat only for the group to wipe on the first boss and disband
Want a fast mount? Have fun grinding.
Want Blessing of Kings? Innervation? etc etc - best get the right talent points
40 man raids - so much afking
There was plenty of things wrong with Vanilla that have been improved now. The reason people loved it and with TBC (myself included), was because for many it was their first MMO and it still had that new feel. TBC raiding was epic - Illidan and Kael'Thas were awesome fights.
Of course the direction WoW has gone now isn't great with Looking for raid etc. But I have no problems with people being able to gear up easier. As I've stated, if you didn't raid Molten Core it was tough to get into any raiding guild as you didn't have the gear and couldn't keep up.
Another reason for Vanilla and TBC being praised highly is the people you played with. I was in a guild throughout Vanilla and TBC and played with the same people, got to know them, met them irl etc. Was a good laugh. Now people have quit - it's not the same playing experience. You're having to join new guilds which is fine, but it takes time to get to know people like you did before.
When people talk about Vanilla being awesome they are looking at it with heavily rose tinted glasses. Many people preferred vanilla but if they were put back in it now they would hate it I guarantee it!
I have palyed on 60, 70 and 80 servers, as well as retail (ofc) from early-tbc to late-wrath. My experiance of the positives and negatives of vanilla I would say is quite impartial. It is not only about the nostalgia.
Some of the strong positives:
Raids where epic in scale (World boss dragons, AQ40 etc)
Good crowd control was required, none of this AOE spam
Open world pvp and long and enjoyable battlegrounds.
Even of private-servers, AV can last hours.
Good zones, lore and music
No flying mounts, means people actually fight for resources
No dalies, no weekly mandatory badge grinds, play when you/your guild wants to
Gear scaling was more reasonable than it is now (resilience, item level inflation)
The disadvantages:
Inbalanced pvp (rogues/warriors)
Inbalanced pve between the classes
Horrible talent trees (lol balance, lol demo)
Respec costs
Organisation difficulty for raiding