As a youth Ron Clarke, BITD, trained for a while with Franz Stampfl and often did 10 x 440y comfortably under 60 seconds. Clarke was never under 4:00 for a mile and I'm not sure he ever got particularly close.
Now Stampfl generally had his athletes "jog" a 440y in ~2min after each rep, so maybe the physiological effects are different from a rest interval of 60 seconds' standing or walking--but I honestly don't think they'd be a whole lot different.
Clarke was on record as saying that it was easy to get revved up for a lap under 60 seconds, but hard to sustain that pace. I suspect that he ran the quarters as a semi-sprint, rather than with his true mile stride--and he had the aerobic talent to take a lap at a slow run and recover almost completely, then go right into another semi-sprint.
As with other training protocols, it's possible to "learn the workout" and become progressively better at it, without necessarily seeing better results in race times. OTOH when Bannister and his training mates were finally able to average 59sec for their ten quarters (also under Stampfl), he had a real feeling that he'd be able to break 4:00 for the mile...so, for some people, part of the workout's benefit--maybe a big part--could be the confidence it builds.
And FWIW I've noticed that other coaches say 12x400 is the criterion workout.