The other thing it has going for it is it encourages immediacy, which makes it fun for sports fans and journalists love it for that as well. Which then leads to the modern "immediacy vs. accuracy" problem that broadcasting faces as well. The main reason politicians like it is because that's where the journalists are at.
I think you're putting too much on Twitter if you're trying to blame it for lowering the level of discourse, or for political mobbing of people online. So much of this is a broader symptom of the Internet being accessible to so many people who are enthused but not very informed. And it happens across platforms. Facebook is worse IMO as it really leads to the lowest common denominator of political nonsense being shared out.
TL;DR: Twitter is good if you want to find people who have common interests. Or want to find out more from celebs and/or creatives. Or just from more normal people who have a cool job. It's bad if you want to talk politics, but so is 90% of the Internet.
I don't think that Twitter was originally designed for real discussion and discourse, but it's become the Social Activist Platform™, and as such, discourse and discussion are almost necessities. In it's current state, however, it's 140 character format unfortunately aids and promotes ignorant and uninformed statements rooted in mob mentality, killing the possibility of any meaningful discussion or discourse, which could benefit many of the conversations that are occurring on the platform.
Twitter wasn't meant for discussion and discourse, but it's community seems to be demanding that it be exactly that.
That's just my (admittedly biased) take.