You undermine your own (good) argument with this bit of hyperbole, which is obviously false. If the FBI somehow had a good-guys-only backdoor that allowed them to decrypt everything, they absolutely would use it to solve a lot of real crimes, from financial fraud to murder. In fact, the majority of their use of the backdoor would be clearly beneficial to society.
But, they would also abuse it. The abuses would be rarer than the proper uses, but insidious, ultimately making the backdoor more harmful than beneficial.
This does not align with my own observations on this matter.
If I look at something like the mandatory metadata retention in Australia, and how it's been used, the vast majority of the cases it's been used are of no clear value to society as a whole. Similarly, no major cases that have been successfully prosecuted since the program was started have been linked with the usage of this metadata repository. There is still no public proof ay clearly beneficial use of this data has occurred yet, several years after having been implemented.
We both arrive at the same conclusion at least, that a police-decryptable stream is likely more harm than benefit, but I feel your assumptions about the good-faith usage of this data are dangerous to make. I have not seen any proof that these kinds of data repositories are well controlled in general... and given how much data could be retrieved using such a system, I would need a lot of certainty that the society gains outweighed the risk of abuse.
So far, none of the governments pressuring for this change have been able to make even a vaguely believable assurance on this point.
The last thing I want is another robo-prosecution system that runs amok and starts flinging out automated infractions and charges. Between speed cameras, stop light cameras & automated debt-collection programs, automated parking infringements, etc we already have way too many.