In larger companies, promotions and role changes are often entirely separate things, and it's not possible to do a "diagonal transfer" that involves getting a promotion and moving to a new role at the same time. Open roles, even internally, have fixed level requirements and a Level 2 Widget Fiddler is not going to be eligible for a Level 3-4 Discombobulator role unless they get a promotion to Level 3 in their current role first.
Whether this is fair or sensible is another question, but the general thinking is that by being promoted to a level of responsibility in one role, they've demonstrated that they have the soft skills (leadership etc) needed for the same level in other roles as well. This is particularly the case for more senior management positions, where soft skills are often paramount.
Short of quitting for a less rigid company, it's unlikely you can do anything about this in the short term. In the medium to long term, you should be working with your manager on promotions that will enable these career opportunities.
Also, large companies anchor their salaries on what other companies are paying. (And yes, this is recursive.) If the market average salary for Fiddlers is higher than Discombobulators, a Level 2 Junior Fiddler may well earn more than the Level 4 Senior Discombobulator.