This system will encourage first-level managers to do everything in their power to be "passed over" every single time. I can imagine the ridiculous shenanigans they'd pull, walking the fine line between not being too competent lest you get promoted, without being too incompetent that you get fired outright. Sounds like the making of a truly middling culture: questionably competent-ish, but not ambitious.
I think I'd watch a Office Space/Silicon-Valley-type show based on this premise. The overachiever character perennially delegated to bug triage, doing endless interviews for a perpetually open position on the team and being sabotaged when they manage to put some real work in after-hours (for comic relief. In real life, they'd get fired)
I do like the idea, though.
There’s no meaningful pay differential for senior staff, so ass-count is the measuring stick.
It's much closer to term limits and the elected-office/civil-servant split in a democratic government. That has its own set of problems, but is generally fairly good at discouraging empire-building. It also differs in that civil servants generally can't transition to being elected officials (despite their qualifications, they face a lot of obstacles to winning elections), while here executives would generally be drawn from the ranks of ordinary management, keeping the ranks under them dynamic.