Wouldn't just having a second key which the government keeps in escrow in case they need to decrypt a message achieve exactly what you are saying is impossible?How would that work? A basic principle of encryption systems is that only relevant parties have access to the secret information. Typically in asymmetric systems they generate their own private key or other secret and never share it with anyone. Moreover, techniques like perfect forward secrecy rely on generating new session keys at each step.
As soon as you mandate a systemic backdoor where someone else's secret can be used to unlock anything, you have undermined the whole premise of the system and created a huge single point of failure.
Not only that, but normally if there is any concern that a key has been compromised then you can change it to at least continue to protect future communications. With this sort of back door, any compromise is permanent.
If you think that's not a serious risk and governments could be trusted to keep such an important back door key secure, let me first ask you this: which government(s) should have access to that key? What happens when, say, someone in the US has family in Iran, and the governments of the US and Iran both insist on being able to intercept messages between them? What happens if a more authoritarian government is elected in Australia and a more liberal one in Canada, and the Five Eyes agreement collapses?
Don't forget that a large part of the reason there is so much public debate about these issues today is because someone walked out of the most powerful intelligence agency in the world with the modern equivalent of a note of its deepest secrets in his back pocket and then shared that note with the world.