Backdoors don't work because yeah, it breaks the whole system. But not everything is encrypted with these companies, that's just plain.
There will always be some sort of secret only the government has access to, and once that secret is leaked it's game over.
All it's arguing, is to say "You don't have to encrypt literally every part of your system and delete the rest" a la what Snapchat suggests they're doing(though we don't have proof).
The only way the government can get the equivalent of a wire tap is if there is no end to end encryption. What police do not want is to need to go back to pre-telephone detective work where they need to determine the location at which the parties will communicate (with modern communications there are of course at least two locations) and compromise that location to spy on the supposed criminals.
I ask this because I'm curious whether you (and people in general) believe that hackability is the only obstacle to giving government access to personal data (with a warrant, of course), or if people would still be uncomfortable with such a system.
Personally, I think such a scheme would be a good compromise, but I'm not a crypto expert so I don't know if it's in any way feasible.
Key escrow came up back then though I don't think it included needing multiple keys in order to decrypt - not sure if that's mathematically possible or if there's another reason that never came up. I suppose to the government that's not much different than still needing to compel individuals for the key.
Your point about companies is interesting since things like iMessage could be MITM currently anyway to get unencrypted content for government requests. I think most people don't necessarily trust the company behavior here though and given the government's recently revealed behavior with National Security Letters and secret, massive, unwarranted data collection I don't think they should get a pass. I'd rather side on the power structure unable to collect some of the information even if they're unable to investigate.
I think fundamentally introducing multiple ways to get keys takes a secure system and makes it insecure - the access no longer rests on one individual's knowledge. In general I think that's a bad idea - it also doesn't prevent people who want to actually encrypt their information from doing so (it just harms the regular public and dumber criminals).
As a matter of interest Shamirs Secret Sharing algorithm (https://en.wikipedia.org/wiki/Shamir's_Secret_Sharing) is quite nice in that respect. The "secret" would be the decryption key. Using Shamirs Secret Sharing algorithm you could split the key into two so you would need both parts in order to work out the decryption key. The government could have a part. The company could have another. Only when both were combined could anyone work out the decryption key.
This would mean neither the company nor the government could decrypt messages until they work together - and therefore reduce the risk of hackers and rogue employees. It wouldn't break the encryption with dangerous backdoors but would allow the authorities to quickly gain access when needed for a specific investigation.
I doubt anyone would ever implement anything like that since it would be (slightly more) complex and you would have to trust that the decryption parts are valid. But I thought I would just mention it in case anyone else might find that algorithm as interesting as I do.
If you have a government entity routinely breaking into companies and taking over access to things (targeting sysadmins) then the scheme doesn't work very well. I think most of the argument behind encryption falls on this idea that it either is secure (no backdoors) or it isn't. You have a spectrum of insecure things you can do that are arguably better than nothing, but they're not secure.
Remember the "TSA locks" we're all required to use on our luggage at the airport? Nobody but the government was supposed to be able to unlock them. But now anyone who wants to ruffle through your luggage can get universal keys for all TSA locks. What happens when that same scenario plays out with your bank account, your company emails, or any online store you've made purchases from?