I don't think paper money is facing any competition from Bitcoin as government is not interested in circulation of a currency they can not control and regulate. Transaction of Bitcoin also charge a high fees which makes its use impossible for small transactions.
Absolutely,
the government has the power to freeze the exchange sites to stop the circulation of bitcoin, without exchanges bitcoin is nothing and if it will be declared as illegal there is nothing we can do. Paper money will remain as it is the most simplest form of currency where we do not need to go online to spend, majority if not all the people can benefit with paper money but with bitcoin it's only a little portion and not even the poor people
Some governments have already tried that but miserably failed
The Chinese Central bank tried something to that tune, even twice but Bitcoin only rallied further and higher. "Freezing" exchanges would likely mean stopping Internet at large (to be effective), but that would be prohibitively expensive for obvious reasons. Otherwise, how are you going to stop something which might not even have physical presence? There are no offices to get raided, there are no bank accounts to get blocked, so how are you going to halt the exchanges? Some countries block access to exchange sites, but there are free VPN's and proxies to easily render all these efforts futile and void
Some countries are better than others at blocking internet sites, but you've correctly identified the best way to stop bitcoin, and that's to target points of exchange. Egypt seems particularly adept at blocking websites, and blocking VPN services operating in the country as well, as we've seen in the last week (non-bitcoin related blocking, but effective to blacking out access to certain news cites nonetheless). I don't know how good the Chinese are at blocking VPNs, but I imagine with such strong state controls over the internet, if they wanted to block it entirely, they would be able to do a decent enough job at it. In January, China reiterated its ban on a range of foreign VPNs, but from what I've read, there seems to be mixed information about the effectiveness of the ban. But Egypt can do it, I don't see why China can't.