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.
Some other examples of recent, useful tweets:
https://twitter.com/TheStalwart/status/775038793376231424
https://twitter.com/cblatts/status/685580497859252224
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.
Other social networks I can think of are mostly focused on sharing pictures and experiences among close friends.
This is what Quora is all about
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).
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).
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.
There's some interesting number is the Pew Poll, particularly the first bullet point:
http://www.journalism.org/2015/07/14/the-evolving-role-of-ne...
How about:
> the media prefers to use Tweets as the minimum unit of cultural exchange
You're trying to discount this, but the media only survives if it reports on what people consider to be culturally significant.