bitcoin is mining. without the miners there is no functional bitcoin. and china has been stomping on the miners for awhile. hasn't stopped them. only stopped large scale mining. bitcoin functions just fine with small scale mining.
That's not entirely correct. It depends on what kind of hashrate is "small scale mining" in total. If it is significantly less than the current level (eg. 20% of it) then bitcoin is in a big trouble because 51% attacks start becoming easy.
Besides the governments don't have to crack down on everyone, they only have to make it illegal for regular people to stop on their own out of fear.