Over the decades, I've played in and run some high level D&D games.
I've also played and run as many non-D&D games that have gotten to the upper levels of advancement supported by the system (like Shadowrun, Classic Deadlands, Ashen Stars, White Wolf Mage, and others).
It is my observation that games for which power growth is an intrinsic part of play, breaking at the upper end is a common, perhaps universal, feature. It isn't a D&D-specific thing, but an issue that any rules framework has a window of good performance, and it tend to fail outside that window. "Breaking" is some mixture of issues of being difficult to prep, bog down in play, have PC balance issues, have initiative= win issues, or the like.
That said, though, I don't think that the major barrier on high-level play is that breaking. I think that the major speedbump is time commitment limitations and limits of basic interest in very-long-running play. I expect most campaigns top out at 18 months or so, regardless of the level of play. Reaching high-level play then would call for starting a game at mid-level.
And I don't know if doing so really serves most folks highest priority goals of play.