I would say it's worked out pretty well for me at least given my career trajectory! Feel free to draw your own conclusions from my resume (it's on my about page).
I think you are conflating "exec attention" with "important projects": these are very much not the same thing.
Fair point. So if you are saying “get on important projects” is the lever, we are in complete agreement.
You can put important projects on your promo doc and if you communicate it well, you are golden. That’s far more important than “executive attention” when it comes to the promotion committee.
Just don’t be the guy who is working on the internal comp tracking system that no one thinks about more than once a year