The disadvantage of anonimity [sic] is that -- well, there are a lot actually, of which just two below:
1. Anonymous people tend to find it easier to be rude (certainly more so than they would be if there were personal repercussions for their behaviour);
2. When it comes to matters where expertise is highly beneficial, there's no way to check whether an anonymous source is genuinely well-informed or is just faking it.
Twitter has real people online as well as the usual crowd of anonymous accounts. Indeed, it sometimes has real people who are at or near the very top (of politics, art, film, science, etc). That could in principle be rather good for encouraging genuine connexion between, in particular, politicians and those they represent.
In practice, it mainly ends up being filled with people either violently agreeing or violently disagreeing with what others say, but never mind.