I find it amusing how people take this 'leveling game' at big companies so seriously. The title they get at these companies become their identity. They live by the rules the company imposes on them. Amusingly almost the opposite of independent thinking, which they are so proud of.
What I found during my career is that some people blossom at these big companies, and some, with equal talent cannot really realize themselves, while they blossom at other organizations, perhaps in startups, or just at more interesting problems. What some people do not realize is that this aspect that as you level at these companies 'you get the big picture more and more' is not really true in a lot of cases. Efficiency and big picture thinking is almost orthogonal. Efficiency is context dependent, high level thinking is less so. I have seen people getting the big picture on things even at low levels or even considered a junior, while people on high levels suprisingly small minded. Higher level at these organizations means that you are more productive in the given field, given organization, for some reason, this can be because of good political skills, because you work your ass off, or because you have a very efficient brain, but it does not necessarily mean that you have better high level vision, or taste or maturity even.
Sometimes it is almost laughable how these people who treat these leveling system seriously and get to a relatively high level treat young colleagues. They are almost naive about how young people think. They think that L3 juniors cannot do anything alone. While I see even young kids playing with suprising autonomy if they are thinking in the right problem space.
True role models of mine never were/are L3, L4, L5, etc... They were/are awesome engineers or scientist from the get go. (Like the Johns: The von NEumann and the Carmack.) Experience lets you get better and better, but if you are stuck at a role or organization, the problem might be that you need to find something that you are more passionate about and not necessarily that you are low level because your thinking is not 'independent enough' or you are not 'high-level enough'. At least that is my experience.