False dichotomy. Of course not everyone has the same experience/skills, but any corporate system of putting individuals to tiers has little to do with experience/skills.
I think they measure different things. The ladder levels have to do with the type of jobs you can accomplish in a large organization. I actually find they translate reasonably well to nontechnical roles in corporate structures. It is of course tempting to think that good engineers will be high level in those ratings, but that’s really not what is being measured by levels. A certain proficiency is required, but it’s mostly about responsibility and ability to take on tasks of a certain scale or organizational complexity.
All this to say it is absolutely reasonable for the OP to complain that they are being underutilized at the role of senior being given small byte sized projects of for no other reason than that this would prevent future growth.
That's just not accurate. I've seen these systems run at multiple companies, and in every case they had a lot to do with skills and experience. It's true that they're not a perfect classification, and I think it's defensible that some people prefer a system where this kind of leveling doesn't happen.
But the tradeoff is that career advancement becomes less legible in a way that other people often find frustrating. Why does Alice get paid 3 times as much as me to work on cooler and more important stuff? "Alice is L7 and I'm L4" is often an easier answer to accept than "Alice is a better engineer than I am" or "People with Alice's experience have more options than I do".