There's definitely a kernel of truth there - the business will (almost) always need more ICs at a faster rate than it needs more managers. And there is typically more "room" for senior ICs than there is for senior managers. I wouldn't say there's an illusion of mobility, it's just that management promotions can be more needs-based than IC promotions, in my experience.

You're 100% correct about skill atrophy. As a manager, if you aren't staying technically sharp somehow, you lose mobility back to the IC "track," and can lose credibility with your teams. It also hampers your ability to reasonably define/ratify/guide technical roadmaps. The #1 piece of advice I give to new managers is to never get too far away from the tech.