[Note this is written some hours ago, before the most recent posts by others. I may have interpreted Chris Abbott's previous post, and I tip my hat to him for scooping me on the "Clipper Chip" point (though not in as many words).]
what kind of system would allow for access with a warrant while also avoiding the "secure against nobody" state?
I ask you the same question. You are the one who proposes the inherent contradiction of a system which is "secure" but for the holes required for warrant access; I believe the burden of persuasion ought fall to those who want those holes.
Moreover, please be reminded that you are advocating that to catch "bad people" doing "bad things", we must give "bad people" the ability to do more "bad things". It is incumbent on you to explain. Me, I believe in prevention in preference to cure (although admittedly, such may foreseeably result in budget cuts for "Skeptical"'s department).
So, how do you proposed to secure a system against all manner of attacks, including attacks by insiders (as discussed by Professor Felten, a warrant is technologically indistinguishable from an insider attack), attacks on the increased attack surface required for any kind of backdoor or "skeleton key", and attacks by insiders within agencies which hold "legitimate" backdoor access---while permitting all this super-duper security to be somehow overcome by a signature and a stamp? Contra popular superstition, black robes do not actually confer such magical powers as could resolve the contradiction by fiat, and black hats do not actually care if you designate a backdoor as "authorized access only".
FWIW, all this reminds me of '90s arguments about the Clipper Chip. Only now, we know that the United States government houses the biggest blackhat gang on Earth. Observation: Any system or network so secure as to resist TAO intrusion must necessarily meet the far lower standard of being warrant-proof.
I do realize that Bruce's point may or may not have been distinct from mine---as is the approach by Chris Abbot and Nick P---yet I argue that the distinction is without a difference, per the Felten essay I linked earlier, and per all those old arguments about Clipper Chip.
I also recognize that I am being used as a foil by "Skeptical" to prop up a failing argument against others here; some might characterize my position as extremist, whereas I posit I am simply following reality to its logical end. A properly secured system provides end-to-end security for communications, privilege and policy enforcement for local and remote access, and protection of data-at-rest against both local and remote threats. A system cannot be secured while opening holes for access-by-fiat by such a bureaucracy as would embarrass Byzantium. Not against insiders, as Professor Felten so cogently argues, and not against anybody else.
(So, how do you stop "bad guys"? In this context, such a question would be a fallacious misdirection as a counterargument; yet nonetheless, it is a question some people might ask. Well, my ingeniously inventive idea is to start by securing everything. Prevention, rather than cure. I also note parenthetically that, as "Skeptical" is most exquisitely aware, HUMINT is quite powerful. Not that I am in favour of it, either: A society of informers and stool pigeons is a society of lies and corruption. I merely make the point, that human intelligence cannot be stopped by technological means. Anyway, most actual detective work does consist of pounding the pavement, talking to people, and piecing together clues from the ghastly mistakes people tend to make. It is wise to remember that before telecommunications existed, telecommunications could not be wiretapped. Once upon a time, indeed, homo sapiens somehow survived the depredations of criminals without hidden microphones, ubiquitous security cameras, IMSI catchers, and a segregated sixth floor within a certain wing at Fort Meade.)