the fact that you took the time to write all that is extraordinaryIs it possible? Yes, obviously. You could just get a scramble that has, say, only outer-layer moves; or perhaps a little less far-fetched, a scramble with the centres already solved.  The top big cubers could certainly capitalise on this and get a sub-minute solve.
Is it likely to happen within our lifetimes? Probably not. A decently lucky speedsolve on a 7×7×7 will still take over 450 moves . You're looking at a sustained 7.5 tps with zero pauses in order to execute 450 moves in a minute. Max's 1:47.87 WR single went at "only" 5.04 tps (STM), for context, and also used much more than just 450 moves.
Future single records are always a bit funny to speculate on, because they're just one lucky scramble away from being broken. My gut feel is that we won't see a sub-minute single in at least the next 20 years , but it's hard to say with much certainty. The biggest source of uncertainty isn't about whether Max Park will get it (he won't); it's whether there'll be a new generation of big cube specialists who will overtake Max, the same way Max overtook Feliks and Kevin Hays a few years ago.
 So, I did a little calculation, and I have a lower bound of 1/2e54 on the chance of getting all centres already solved on a random-move scramble. That's 23 orders of magnitude more likely than with random-state scrambles (1/3.61e77), though of course it's still very unlikely in absolute terms.
 Unfortunately, I don't have move counts for 7×7×7 solves available, but I do have my own stats for 6×6×6 linear slow solves (~330 moves), and that's about 1.5 times the 6FMC UWR (226 moves). If we extrapolate this to the 7FMC UWR (313 moves), that would mean unrealistically efficient 7×7×7 solves would take ~470 moves on average. (This is very handwavy and is not at all a precise calculation.)
 Under conditions similar to WCA comps, so using computer-generated scrambles, using a proper timer, etc.
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