I honestly think this mindset creates what I call "The Reverse Peter Principle". I've seen this happen when very inexperienced leadership implements this system based on hype from other companies. You end up having a lot of engineers doing random stuff that's not part of their job description just to try and get noticed/promoted, and nobody is punished for shirking current duties as long as they aren't just completely slacking off or something. You stop getting rewarded for doing the drudge work and crushing your current role, because you start focusing on the future over the present.

I think it all mostly boils down to skilled versus unskilled managers and internal career planning. If a manager is promoting people who aren't able to execute on the new role more often than not, then they are bad at recognizing when people are ready for more responsibility, and they should work to improve that skill while also working to plan things better with their reports and set expectations. To me this doesn't say that there's a fundamental problem with the system that needs to be alleviated through process change.

And on the flip side a skilled manager would be better able to keep everyone on task in their current role even while they are planning/demonstrating for the next role, if you're doing the "no peters" thing.