You don't think either of those (completely off the cuff) examples would make use of high level abilities? I just said high level abilities would not automatically negate those kinds of adventures.
What do you think high level.PCs should be doing that they can't do at lower tiers?
Using high level abilities.
When PCs advance to the higher level they gat access to abilities, often magic, that trivialize many things. As discussed above, many DMs tend to try to negate or limit these capabilities in order to run a games that are like lower level games. When the DM does this, they often prevent the higher level PC fromn using their powerful abilities by saying that they just don't work, or someone has some countering magic, or some other folley. Rather than celebrate what makes a high level PC different, they attempt to make the high level PC fit into the cookie mold of a lower level PC.
He may have been prepared for other options, but what actually happened (and what we all saw) was basically a big standard 5e combat. The takeaway from that example is that high level D&D is the same game as always with bigger numbers.
Absolutely not. One result is not indicative of all results - and that is exactly the mentality I counsel against for enjoyable high level play.
Don't get me wrong. I expect there to be high level combats filled with powerful abilities at high level. The players have many routes and options at higher level, but combat is going to be an often executed option.
However, when it is, it isn't just bigger numbers. The nature of the abilities change the combat. There is no lower level, "You just die" spell. There is no equivalent to Foresight or Timestop. The high level magics - and high level abilities of many of the classes - change how the game works. Your argument was mostly true about 4E - it was just a numbers game there - but not true of 5E, 3E or earlier editions. The game is designed to change in how it functions as higher level abilities are accessed and new opportunities arise.
If you're running high level games and they work - great. If you're finding your games fall apart, consider rethinking your approach as I've suggested to see if you're leaving opportunity on the floor. Essentially, if you ever negate or lament the abilities of a PC - you're not creating the environment that I've found best supports high level play. If you celebrate how awesome the PCs are and how much they can achieve and let them achieve those things ... and oppose them with larger problems that require solutions that they have to assemble ... well, it works really well.