Could this principle be applied to encryption? A cryptosystem for personal communications carefully designed to be crackable using certain amount of resources. So getting access to one person's data would cost you say $1000 of cloud resources. And first you have to obtain an escrowed hash to crack using a warrant.
Would this be acceptable to public?
Much as you can build a physical policing system with or without oversight and with or without covert powers, you can do the same for encryption. It is absolutely possible to build a system where the company, the police, and the courts all need to agree in order to hand over access — in fact it's more possible than with physical security. It's also possible to build regulatory bodies that make relevant details publically visible.
Compare that to remote backdoor access to everyone's encrypted communications. All they have to do is push a button in order to instantly get access to someone's mail, calls, instant messages, social media, phone location history, etc. Abusing this power is a trivial matter and there is little if any oversight. The Five Eyes intercept, decrypt and store even their own citizen's communications as a matter of course and will tip off law enforcement so they can parallel construct a case using means of investigation that are actually legal. Intelligence employees have been known to abuse their powers to spy on their significant others, a practice that became known as LOVEINT. People who are a threat to those in power -- political opposition, whistle blowers, journalists, dissidents -- will probably be targeted despite their rights to privacy.
In order to obtain encrypted communications, police forces should have to get a warrant and obtain the physical storage media that contains the messages they want.