They might eventually, but even then the pacing makes it different. Compared to something like the a Mythic+, where there's not only pressure to get it over with because you are just looking for the carrot at the end of the stick, there's even reward for doing stuff as quickly as possible. Classic promotes a slower gameplay and playing "safe" more than it does "getting things over with", because it's worth it to deal with packs of mobs slowly, it's worth it to wait for the healer to drink, rather than risk having to wait for people corpse running.
Will this change as people get better gear and used to run the same dungeons over and over again? Probably, yes. But in Classic there is an end goal. There is BiS gear for your character, and eventually you will get there. You won't be running a weekly gear slotmachine hoping to get an upgrade that actually only has a tiny small chance of happening for 2 years, with every patch making the previous gear completely obsolete by introducing slightly better versions of the same gear. Also, you can only inspect people after you are phisically close to them, and even then you can only see their gear. There's no achievements, no armory or API. It's very possible there will even be addons like gearscore or similar, but even then (having played years ago on a WotLK server where gearscore was popular) it was fairly more forgiving.
Classic encourages player to help each other because of how mistakes are punished (corpse runs and such) and what a pain it is to replace people. Not only is it harder to find a replacement, it takes time - usually more time than just trying to help. When it's easier and faster to kick and find a replacement, people will just do that, even in Mythic+.
Yes, the M+ plus system of getting "locked" once started is kind of similar to Classic, but feels jarring compared to the rest of the game. That's one of the reasons, I would assume, why the community gravitated towards continuing pugging using the armory and raider.io instead of generally trying to find stable groups of people they can run with. It's also why many people are more prone to abandoning what they deem to be a "failed run", or to kick someone who they deem to have "doomed" the run, and just go level up a different key, instead of actually trying to help that player, or try to make the best of it, simply because it will take less time.
It's also very hard to justify investing time in helping someone whom you will never see again. In Classic with pugs being from your realm, there's a high likelyhood that you will find people who you helped down the line.
Social interaction isn't just about having conversations. Is about the whole process of playing with that person. Yes, many people will still be silent even in Classic, there's still diferent personalities at play and some people are simply shy even in Classic. With that said, the single fact that you actually have to whisper "hi, inv", or ask what quest the others are on, starts that engagement. For many people that is a necessary "kick" to get over that barrier of actually typing and start communicating with the people who you are with.
That's only helped by the fact that you are all in the same realm and players are not easily replaced, it makes it much easier to treat the other players as other players, instead of disposable means to achieve your "singleplayer-like" goals.
I won't pretend this is exactly why, or that I know exactly why, but I certainly have experienced it. There's no guarantee at all that you will have amazing interaction with every person you group with, for sure, but there's certainly a much higher incidence per time played in Classic than in Live, from my experience and seemingly from others' as well.
Not really, just like the lack of that "toxic" nature does not promote the non-existance of social interaction in pre made groups and guilds. The majority of players who prefer to play in guild are already doing so. The players who like to play in pre-made groups either already have one, or will find a hard time finding people to join.