Many (most?) important computer systems use UTC precisely to avoid time changes like the DST transition. Just one example that comes to mind is that DST can cause important cron jobs to repeat, or not occur at all.
Right, which is why it seems like the obvious thing to use TAI as the underlying base time in a computer system, and have UTC be just another time zone offset on top of that, so you don't have to deal with leap seconds either.
Exactly. The underlying clock would store actual seconds since 1970, and when you request UTC it would add the current leap second offset. Which is more or less how GPS does it already, for an actual working example.