In a few ways, the hurdles you outline are a helpful filter management skills. Presenting and promoting your team's work will become just as important as doing the work. Providing context for failures, which could be seen as covering up, is critical. If you are too busy working to prepare an important presentation, you are not ready to be a manager.
Even if the promotion keeps you at an IC, your responsibilities are still increasing, so I think most of those points stand.
Is that what is being promoted in a presentation to a promotion committee arguing that you individually should be promoted within the organization?
"... too busy to prepare an important presentation..."
Important to whom? You or the people you are working for?
I agree a system like this could filter for what we commonly recognise as "management qualities".
Although I am not sure they would be qualities such as selflessness and putting the needs of their reports and the organization ahead of their own aspirations.
If you can't advocate for yourself, how are you going to advocate for anybody else? A promotion process, if there is one, is an important time for you and the organization. Lots of people's time is being spent to figure out whether to elevate an individual towards a position of company leadership. In the long run, it's far, far more important than any individual project you might be working on (and if it isn't, show that you can get yourself out of the front lines, or you are destined to fail at management).
Even if the promotion keeps you at an IC, your responsibilities are still increasing, so I think most of those points stand.