Maths doesn't work that way.
Universal escrow == universal access. Leaking == global compromise.
There's a place for personal recovery key quorums, where multiple parts are joined to create an alternate recovery key, but that involves key management for each such key served, which is a Very Large Problem.
Might be possible to take it on, but the underlying problem of identity remains: The question "who are you?" is the most expensive one in information technology. No matter how you get it wrong, you're fucked.
Deny access to the right party: fucked.
Allow access to the wrong party: fucked.
The only advantage of security-based DoS over security-based unintended dislosure is that denied access doesn't propogate. Published data cannot be unpublished, at least not at any reasonable cost:assurance level.
Because of the key management issues, most seriously-proposed data-backdoor systems revolve around one or more of:
- Workfactor reduction in which known keys or values are used in key generation. The resulting keys are weak where the known inputs' secret elements are known, at least to state-leve actors.
- Specific escrow keys. No workfactor, just key access. Widespread key access is a Very Bad Day.
- Specified access accounts. Like above, but worse.
- Specific system bypass. Alternate paths to data access on systems.
- Alternate data submission. Various "phone home" or intercepts of in-the-clear transmisions, either through design or software/device compromise.
As a practical matter, alternate information channels (usually metadata), public data, standard detection, bug/zeroday exploitation, and various sideband attacks (Maginot compromise: don't go through, go around) tend to be used, though cryptographic attacks have some utility.