This is roughly what I've been thinking, though I would not advocate the use of transmute. I think the missing variable is the fate of const fn. We've talked many times about removing as in favor of more specialized methods, but settling the story around const fn was always the blocker. My inclination right now is to leave as the way it is. I do not consider it deprecated, as there is not yet a suitable replacement, but I think that we should build up better replacements and perhaps we will be able to deprecate it in the near future. This might be the cast operator, which I confess I was fond of, but I'd be happier if we can do it with methods rather than adding a new operator.
(As for numeric casting, I could imagine having two sets of methods, one that is only for widening, and hence infallible, and some variant on the existing NumCast, which permits arbitrary checked conversions.)