I suppose the liability, if so broadly interpreted, would fall on the miners, but only if it could be proven that they won a block that contained a transaction used for illicit purposes.
The interpretation that somebody is liable for mixing at all, with no illicit use proven within the transactions, is probably questionable. The miners are also not receiving dirty money as compensation, so even more so.
And even with illicit use shown, laundering can happen with just about anything you can buy and sell, so, unless every retail store is doing KYC, then they could also be exposed to such liability.
Above all, I don't know if coercion is a successful long-term strategy for defeating privacy coins. Even for criminals, the value must tie back to average citizens purchasing it from them, and even with no enforcement they would not want to be part of that, and the value would collapse. If a privacy coin does have value, it reflects political fears of the average citizen, and aggressive enforcement unaligned with common values may actually increase its value.
The dollar system is the most valuable partially because it does enforce common values, and permits all else within. But obviously not everybody believes that this is guaranteed in the future.