Mining, on the other hand, is decentralised. By "banning" mining, they would be banning something which could happen in any home anywhere without their knowledge, so it would be a very ineffective law.
Oh really?
Yes.
There is nobody mining at home in China
Pretty bold statement to make. But you can't get any statistics about that - because mining is decentralised. Sure, miners are loud, but my point is that in general it's a futile battle for a government to have, expending resources to get people who aren't ultimately wasting any money, and expending a lot of resources trying to get the people who do it on a smaller scale.
It would also really piss people off, because it's basically stealing their investment into those miners by forcibly shutting it down. Shutting down exchanges, on the other hand, isn't a huge threat to people's investments unless people's coins get stolen from the exchanges.