Why would they want to control Bitcoin? In the grand scheme of things, Bitcoin doesn't really affect them, if at all.
chinese people casually moved $50 billion in crypto outside the country last year:
https://www.cnbc.com/2020/08/21/china-users-move-50-billion-of-cryptocurrency-out-of-country-hinting-at-capital-flight.htmla big chunk of that was bitcoin miners.
the government recently cracked down on shadow banks and foreign real estate schemes as avenues of capital flight. bitcoin must be a big thorn in their side as it soaks up the demand from those channels.
in theory, if they control the mining network, they could freeze/censor transactions they believe are linked to capital flight. it's quite a paranoid theory but it makes slightly more sense than just outright 51% attacking the whole network or something. there's no point in that, as hash rate would just leave china and the compromised pools.