>but a back-door exists that allows anyone with access to it to bypass the encryption

The trick is you don't do that. Ideally you would only want people with a valid warrant would be able to also decrypt the message (bypass the encryption). So the problem is that you want to design a system where this is possible. Perhaps it takes the cooperation of someone from the government and someone from within the company to verify the warrant. Perhaps you have a list of people who need to cryptographically sign the warrant.

It must in no way be possible for any of these companies to ever run a non-verified decryption mechanism on any single server, computer, or other type of device.

There are so many moving parts to manage, infinite possibilities for abuse, and it would require an absolute massive amount of trust in companies with numerous convictions for abuse of precisely that.

I disagree, I believe that we can still have encryption and catch criminals based on encrypted communications.