You encrypt the message twice so that either the intended recipient or the government with 5 HSMs can decrypt it.
What if you simply claim to encrypt it twice, but instead place random noise wherever the "encrypted for gov't" data should be? If the system works as intended, it shouldn't be possible to attempt decrypting it (and thus verify if you encrypted it properly) without a search warrant based on probable cause, as the key material would be in escrow and not accessible to anybody including law enforcement and intelligence agencies before a warrant is served.
So you can't have proactive detection of that and everybody who wants to ecrypt communications with criminal intent can and will continue to do so with the same consequences as right now, where they can be pressured to reveal the keys but their communications are otherwise secure; the process would risk the privacy of honest citizens (in case if the escrow system is broken) but not hamper the bad guys at all.
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.
This story should be repeated whenever anyone brings up 'solutions' involved with key escrow. Bruce warned us in 2006 this was a backdoor, ten years later, we find that not only was it implemented by Juniper, the backdoor was backdoored by unknown (and potentially malicious) actors. Really, this should be the last word on why this key escrow and general cryptographic backdoors are a terrible terrible idea.
In other news giving someone root access to your machine gives them root access.