I'm assuming that bad guys can modify the software they use, which seems to be a reasonable assumption supported by practice.

And given the proposed rules of key escrow the government has to assume that they use it as-is, because doing traffic inspection to ensure that they really do so is impossible without a specific warrant, so whenever they do get a warrant and get the keys out of escrow, then that's the first moment when they can tell "ah, we actually can't decrypt Bobs messages because he's not using that key".

So the proposed naive system of simply "encrypt the message twice so that either the intended recipient or the government with 5 HSMs can decrypt it" won't work. You can have a more complicated system that works around my objections above, but that would be a different system that will also have other drawbacks. Cryptosystems are very hard in general, all small details matter, a random proposal that hasn't undergone significant expert analysis has almost 100% chance of being fundamentally flawed, and doing reasonable escrow will have all kinds of "interesting" consequences and potential attacks, I am not aware of any public proposals for the specific details of a mass-escrow system that would have reasonable consequences.