This mentality through most of my career has left me trapped as technical support, and it's damn near impossible to climb out of the pit I've dug for myself. What you say about being seen as a car mechanic is true.
It's a tough balancing to make sure you sell yourself correctly and fight to work on things you want to!
To prove the point we put him on a strategic rewrite and gave him master/trunk while the entire team moved to a feature branch for 6 months. This was complimentary to his ego as he was sick of us bureaucrats in the rest of the team telling him what to do and being such a burden on his genius creativity.
By the end he was unable to build / run his own branch, while the remaining team lost no velocity and was making regular releases to end users. The choice was easy at that point.
Compensation has been decent with this approach over the years. I could have made more staying longer in a darwinian bigco but the work was not fulfilling.
By far the easiest way to do so will be to find another job. If you can't do this, yea, mentality will lock you in to positions you don't want to be in.
Fixing things only gets notices by coworkers and good managers.