No, it's not doomed to be centralized in China.
Scenario 1:
The government will take over and continue to mine most bitcoin. They still cannot keep it to themselves because they have to cover mining operation related expenses. They have to sell/trade it somewhere and they cannot prevent anyone who bought from them to send it anywhere else in the world.
Not necessarily! If a particular government wants to ruin bitcoin. They can take over all mining ops within their country and run it by paying out of their pocket. They won't necessarily have to sell those. The intention of the government is what matters, not money!
The last time I checked the mining processing power of China, it ranges from 60% to 70%, that means 60%-70% of newly mined bitcoin is born in China but with this data I don't think they can centralized the totality of bitcoin. However @Avikz is right, if the government wanted to do so then they will target these mining farms, put a tax on it and ruin the mining system. To be honest, they cannot do it anymore since there are only 2.5++ million of bitcoins left to be mined it isn't enough to control the bitcoin by any means.
Scenario 2:
The government will take over the mining farms and shut it down. Bitcoin will still thrive since anyone or any group can set up their own equipment and start mining bitcoin unless if they are in countries where it's forbidden by their law to mine.
They cannot shut it down easily especially when the registered place is just a home, they cannot get inside unless there is a warrant. What I think they will do to go after mining farms is that, they will raise the electricity rates so miners will get a hurting part with mining because the cheap electricity price in China is what makes their miners go crazy with bitcoin mining. Formulating a law that prohibits bitcoin mining is such a foolish reaction, there is no harm that any people could get in mining, so why would they?
