I wonder how often these close calls occur. I was on a flight a few days ago and using an app to track my flight while on the plane. We were at 32,000 ft and according to the app another aircraft was headed straight toward us at 33,000 ft. Just before the two planes overlapped on the app, I looked out my window and saw the other plane go right above us. It was absolutely insane how close it appeared and how astonishing a 1,000+ mph speed difference is. (If you're curious which flights: DL75 and TK1344 on Feb 1, 13:04:20 GMT).
My understanding is that planes passing this close to each other is relatively common, as 1,000 ft is the minimum vertical separation for RVSM airspace, but I was still surprised that the other plane was directly above us and that some sort of optimization algorithm isn't used to maintain horizontal separation as well just in case there is an error in communication on the flight levels.