How does Bitcoin get over the capital controls problem? So, people now talk about Bitcoin as a store of value instead of as a currency. I'm confused as to how central banks will respond to this? Right now, bitcoin is not widespread. Assuming bitcoin becomes more used by financial institutes and ordinary people and starts to be comparable to Gold as a store of value (in terms of number of users), wouldn't central banks lose capital controls? That would be against the interests of every government on earth and wouldn't that create a huge incentive for governments to ban bitcoin? Thanks.
Bitcoin is hard, but not impossible, to censor so if governments really wanted to censor bitcoin transactions they could do it. Right now governments seem more interested in wooing bitcoin related businesses to their countries because they see it as something that can contribute to economic growth. But, yes, if they changed their minds they could shut it down. 

However, what would happen if they shut it down? Would developers and users just give up? The answer is that we won't. We'll switch to crypto currencies that are even harder to shut down. Crypto currencies with anonymous ledgers like Monero. I don't think governments want that to happen. At least with bitcoin the ledger is transparent. 

There is a historical precedent to this. Bitcoin isn't the first attempt to make a digital currency. I suggest you read about digicash and the problems it encountered getting traction. If governments push people will push back!