> [...] arguing that “it can’t be done”, which is of course theoretically true if the goal is to have zero additional risk by introducing a third party [...]
So then you recognize that "exceptional access" mechanisms necessarily weaken a cryptosystem, which are already notoriously difficult to implement securely. This brings us back to your OP, where you complain about people telling you the truth you already recognize, and make two entreaties for assistance from HN:
1. "Perhaps HN would do well to ask how to solve the problem from a technical perspective, given the requirements. This includes both how to build a better mousetrap (one that doesn’t have a “backdoor” or significantly weakens the encryption mechanism) [...]"
2. "[...] and how to solve concerns about abuse of exceptional access."
I understand now that you suffer from severe cognitive dissonance with respect to the first. You just acknowledged that the "weakening issue" with "exceptional access" cannot be solved, yet still argue that it can be solved, presumably with more effort from security professionals.
I already addressed the second: Concerns about abuse of "exceptional access" also cannot be solved, except by avoiding their inclusion in the first place.
Your idea is also a non-starter. Human political masters will set the work parameters, not users (otherwise: Who would choose anything but an infinite amount of work to decrypt their communications?). Users would have no way to verify the work required to decrypt as, again, they cannot verify that communications have or have not been "exceptionally accessed". The work parameters must be updated as technology improves, so there must be a way for human political masters to update work requirements (potentially reducing them). Nobody outside certain SCI or ECI compartments has any idea what kind of cryptanalytic power USG can bring to bear. Maybe, like Skipjack, the proof of work cryptography is subtly weaker than expected in a way that only they know. Maybe the USG will just start allocating $100B/year to routinely use "exceptional access". And certainly, after such a backdoor scheme is deployed, LEO and IC will howl that they cannot access enough plaintext to stop child molesting terrorist superpredators, and anyone who would just think of the children would support reducing or eliminating the burdensome computational obfuscation parameters. Once again: Any such "exceptional access" scheme necessarily reduces security by inserting a critical dependence on trust in humans that cannot be verified and whose compromise has Biblically enormous value to many groups.
> I agree that having a trivial way for governments to access encrypted comms at scale is bad; I don’t agree that governments should be completely locked out, without exception, of all comms deployed at scale by mega tech corporations.
If we agree on the first part, then we should agree on everything that I've written. "Exceptional access" schemes only make sense for unconstitutional dragnet surveillance purposes and are a severe threat to liberty. If a target is known, and is found to be using cryptanalytically impenetrable cryptography, targeted physical surveillance will defeat that cryptography every time. If some impenetrable communications happen between two non-targets, it doesn't matter that those communications cannot be read, because the government doesn't want to read those communications anyway--right? Of course, serious criminals and terrorists--the ones on whom collection is really important for security--are not going to use known-compromised cryptosystems when non-broken ones are already ubiquitous. Therefore this "exceptional access" is only useful on the average citizens; unless, that is, the government is doing dragnet surveillance and attempting to "winnow" out secure communications, something they can only do effectively if they attempt decryption of every "exceptional access-enabled" communication.
Finally, consider your request in the historical context. For the great deal of our history, communications have defaulted to being private (there were no microphones in Lincoln's log cabin) and inaccessible to government agents except through testimony (which cryptography does nothing to prevent). Now your claim is that the government must have the ability to access any communication. But why? Our government and society worked just fine without substantially all communications being recorded and accessible to the government. Such a large shift in the balance of power will, I fear, lead inevitably to tyranny.