Is there any evidence for this claim that a Tweet has more "cultural significance" than a Facebook post with objectively higher engagement?
I think this illusion comes about because the media prefers to use Tweets as the minimum unit of cultural exchange, so Twitter receives attention as the medium in which these exchanges take place - even though it isn't, really.
There a lot of people I follow on Twitter who value their anonymity, like https://twitter.com/pseudoerasmus, and being able to see them debate others real-time about issues of substance is valuable to me.
Twitter encourages interactivity in way that Facebook does not (though that might have more to due with the existing userbase than the UX), and it's text-focused in a way that Instagram, Snapchat, etc., are not.
Why do you think that conversation couldn't have happened on another social network? Specifically, I find that the character limit always makes any actual discussion very hard on twitter. Anything deeper than pop culture and I don't have enough space.
Facebook is a walled garden w/ no anonymity. Privacy (specifically, most posts are only seen by friends of poster) can be good but it can also stifle discussion. Google Plus might have been good (and got some notable adoption among academics initially) but could never accumulate enough of a network for a variety of reasons. Reddit actually has a lot going for it for these purposes, but doesn't work well for "personal brand" building, so doesn't get much uptake among experts.
Other social networks I can think of are mostly focused on sharing pictures and experiences among close friends.
I don't understand at all why you think that is the case. I don't even spend that much time on G+, but I get linked there every once in a while and I've seen plenty of discussions of equal or higher quality (generally higher, because the character limit is incredibly damaging to quality conversation). Obviously Twitter has more by volume, but the assertion that that kind of conversation is even close to unique to Twitter is really bizarre. Hell, I've even seen conversations of that quality on Facebook occasionally (and tons of times on smaller boards). Even complaints about lack of anonymity on G+ (and certainly on smaller boards) have been based entirely in ignorance for the last several years. It's really easy (and policy-compliant) to make and use a pseudonym on every network I can think of that I've seen high-quality conversation on (with the possible exception of Facebook: I've never tried pseudonymity there).
G+ was good (a lot of academics were using it heavily for a while and I think John Baez, for example, still is), but it never accumulated much of a userbase (the reason I don't spend much time on it and probably the same reason you don't).
I don't think the character limit is a boon. Sina Weibo removed it, and that seemed to go well.
edit:
One thing I forgot to mention: I use Twitter lists a lot and have various ones assigned to different fields (econ, genetics, politics/current events, microfiction, etc.). Twitter search can filter by list, so, eg, I can see any idle comment any of ~70 economists has ever made about: real business cycles, endogenous vs. exogenous effects, moral hazard, regression discontinuities, etc., at least on Twitter. I can't really do that on Facebook (no real search, right?) or G+ (might have something similar but not enough people using it).
Twitter certainly beats G+ and the boards that I like in terms of quantity. I just took issue with your claim that you can't imagine conversation of that quality taking place on another network. That's a much stronger claim than "Twitter has a higher quantity of good conversation",whjch I don't disagree with at all.
Yeah I was skimming replies and didn't notice the thrust of your comment. But I stand by my statement about that particular conversation.
Based off what I've seen, if Twitter goes under, I expect one of the participants (pseudoerasmus) would not switch to another social network and would just stick to blogging.
I would say yes then. The fact that the cable news media prefer it gives it more "cultural significance." However even though Twitter "breaks news" newspapers still set the agenda.
There's some interesting number is the Pew Poll, particularly the first bullet point:
I think this illusion comes about because the media prefers to use Tweets as the minimum unit of cultural exchange, so Twitter receives attention as the medium in which these exchanges take place - even though it isn't, really.