Well they did in Egypt
Syria has also blocked the internet for periods of time and Wordpress sites and the like.
I am not a computer expert so I don’t know how easy it was/is for protesters to circumnavigate these bans. I think in Egypt they also shut down the telephone network at least for a time.
@filmfann is right though, this is pretty standard fair. Try to shut down or control communication. An argument for not blocking such sites means if the authorities can monitor traffic on Twitter and Facebook etc., they may have a clearer sense of what is coming.
From a democratic perspective though, no. They shouldn’t. When considering countries like Egypt and Syria etc. we aren’t talking about democracies, so what should happen by our standards doesn’t really matter.
There are/were moves to bring in an Internet filter. The argument is it would only be used to stop child porn and the like. In truth though a lot of pornographic material is not trafficked through the websites this filter would target. It would be very easy for a government to use this filter to shut down websites it didn’t like. All sorts of censorship debates have been happening here about whether such a filter should be implemented. I don’t for one second think they are considering blocking Twitter or Facebook. However, lists that have been leaked about websites that would be targeted show there are websites on the block list that are not of any threat to the government or have nothing to do with child porn.