Like -- I don't know, but is it actually important that the solar day is tied to "wall clock day" so snugly? So what if it's a couple minutes off...?
Even when you're assigned a correct hour-aligned time zone, you'll be off by an average of 15 minutes! Wall clock time just fundamentally has never been precise enough for leap seconds to solve a problem, by two orders of magnitude.
Better to design in the requirement for all software to support these shifts, like a random 10 minute shift every day. That way nobody will write software that doesn’t support the shift.
Some timezone changes are well published before the change and others are published after, and software has to pick up the pieces.
I'd imagine a 15 minute jump to recenter zones would be published with at least as much notice as changes to DST rules.
Though I wonder what happens with the international dateline -- would it shift around the world, or would the UTC offsets get larger and larger? I imagine the latter would eventually also result in software issues when the UTC offset starts exceeding 24h.