That’s what double clutching is for! (Not really, but it can give the synchros the time they need to do the job if you HAVE to skip a gear for some reason)

Yeah, the clutch can only manage discrepancies in speed between the engine and the transmission’s input shaft. But during a gear change, there’s a difference in speed inside the transmission between the input shaft and the output shaft when you move from one gear to the next. It’s the synchronizer’s job to ease that…

Not sure how other transmissions are designed, but in a S2000, if you skip-shift regularly, you are going to destroy your syncros eventually. This has nothing to do with rev-matching. https://www.s2ki.com/forums/s2000-under-hood-22/someone-explain-why-skip-shifting-bad-1026367/