I largely agree but I really think you're missing one major component.
A high-level party has history. They have allies, enemies, and adventures all. They have done wild things. And higher level play is usually predicated on this very history.
Enter an Adventure Path for T3 to T4. This Adventure Path is difficult to write, primarily because of this history. And I don't just mean with the players now, but with the game world. Introducing a specific dark empire into every game is difficult, or a specific big bad. And since D&D encourages people to change settings as they wish and to homebrew their own -- a good thing, btw -- it is even harder to make a high level adventure that people can easily use in their game.
This isn't an absolute problem. It is still possible to write around this in numerous ways. And I think the culture of the contemporary TTRPG table is moving towards a solution already. Games these days are shorter. While years-long games still happen, the average game doesn't go past a year. Many games don't outlive a season. With this, we can divine a trend that smaller stories are going to become more popular. Adventures that can be played in a season with different people or different characters, IMO, will become more attractive then playing the same character from 1-20.
This is all speculation for me. While I know for a fact the average game doesn't go past a year, I'm too lazy right now to find my source.