Well, and that's a major part of the problem: Even if you continue doing better and better work in your current job, you will never get paid more for it. If you want more pay, you have to seek a promotion, and the only jobs that get paid really well are management jobs.
Frankly, this smells a lot like a continuation of the old feudal mindset, where the people who tell other people what to do are considered to be more worthy, more valuable, better people, than the people who just...make things with their hands.
There's really no inherent reason why the person who is coordinating my team should be considered to be more valuable than me. And there's certainly no reason why the organization should consider me qualified for that position just because I do this one really well: management is a different skillset, that one doesn't naturally gain just by doing a non-management job really well. (And I can say this with some certainty, because I have seen both very good and very bad managers, and the difference is night and day. Not just on the morale of the people they're managing, but in the results of what they create.)
If it pays more money - yes. Even if it does not, you can leverage position and find a different job with said new position that does pay more money.