Not much?
In the event that some jurisdictions with aggressive regulators try to impede mining, it will migrate elsewhere. Only if all mining is made illegal everywhere would it be a problem, and that's equivalent to a worldwide ban on Bitcoin, at which point it doesn't matter anymore.
So, in the countries where mining, and presumably Bitcoin in general, has been banned, do you think Bitcoins will have any value?
I was referring to the gathering of transactions stage, which is arguably the expensive part, bandwidth wise. If blocks are represented efficiently (eg, list of hashes or deltas against remote expected blocks) then almost all your bandwidth would go on receiving transaction broadcasts, and that doesn't require Tor.
...which means if I want to prevent mining behind Tor, all I have to do is fill my blocks with transactions that I haven't relayed to them. On the other hand, if it's a rule that you only mine to extend blocks if the transactions were broadcast first, anything that even makes transaction propagation slower, like a bunch of fake nodes, but far from 100%, causes orphan rates to jump. Not to mention I can make it very risky, due to orphaning, to mine blocks containing transactions that a large fraction of the nodes out there have decided to blacklist for whatever reason. You also create new forking risks if transaction propagation is ever prevented, when block propagation isn't.