"but you won't see me flying anywhere near Russia/Ukraine anytime soon"

Actually most flights from Europe to East Asia fly over Russia now while carefully avoiding Ukrainian airspace.

So if you really need there and want to avoid Russian airspace, you'll have to fly via Africa or Americas or possibly transsiberian rail.

By glancing at flightradar24: Everybody is scared to fly over Ukraine, except for Russian (Transaero) and some Turkish planes bound to Russia who fly over central Ukraine just fine.