It's bad for the central banks supposedly but what's to stop the central bank purchasing enough to control the markets?

Cool, let them do it. They will drive the price through the sky. If they choose to not use their bought coins they will reduce the circulating supply while simultaneously having added whatever amount of liquidity into the market. Anyone who owns even a tiny amount of BTC at that point will be very well off. If they instead choose to use their bought coins or resell them, then they also give up their control. In either case, they can't do shit other than join the game like everyone else.

They have no control over the total supply, that's the only thing that matters.

For the same reason China's hashpower is irrelevant. If they choose to fuck with the blockchain (e.g. censor broadcasts of transactions) then everyone else will just fork off and ignore all of China's hashpower.

All while secretly pushing it as the new dollar.

They can't. The dollar is a fiat currency with unlimited supply. Bitcoin is limited in supply and they have no control over its issuance. They can not do anything without benefiting all Bitcoin users in the long run.

If they want to save fiat and their control their best bet would be to do nothing.

If they want to ensure that they won't end up with nothing they'll be forced to relinquish their control and join the party, which will level the field as far as financial markets and currency str concerned.

Maybe bitcoin and crypto is their plan to replace cash?

Pretty terrible plan then, because Bitcoin is designed to cuck them out of any such aspirations. The closest that gets to your worries is a fork called Bitcoin SV. Craig Wright (delusional sociopathic fraud) openly talks about making everything transparent and traceable, which is the opposite of Bitcoin's whitepaper and hence something the DS could be into. The market has long decided that it won't be having any of that shit though.

What gives it any true physical value?

The limited amount (scarcity) and the fact that you require specialized hardware and lots of energy to mine Bitcoin. Getting those things is not free, it's expensive. And costs must be covered. This gives Bitcoin a minimum value in a small interval around the mining costs per Bitcoin. Said process also secures the blockchain and validates transactions, hence, the second source of value comes from the payment processing aspect. Over time, there'll be more effects that increase the minimum price. Bitcoin will be used to fuel the equity markets of the not too distant future. Thus certain portions of savings and assets will too drive up the value of Bitcoin.

I would find it naive to think that they are not behind it or atleast control enough of it to manipulate the market.

Definitely worth considering. But when you do this carefully you'll find that they've almost certainly been screwed. Be it by their arrogance, ignorance or complacency.

As with anything within the mortal realm, their time has come to an end.