Hello. I believe I can be of help to you with this issue.
You are working in a pathological system. By this, I mean that the management has no understanding of what 'causes' human behavior and the firm is suffering because they literally 'don't know what they don't know'. What management should be doing in your case is evaluating both supervisors and their supervisees based on highly measurable performance criteria that includes amount and quality of productivity. Maybe bring in an external consultant to review performance independently and blindly if necessary. Rewarding people for performance and recognizing them regardless of their status will actually cause case productivity to increase and profits of the firm to grow.
If this is a relatively small, private firm and the principals have close personal relationships with many supervisors, and have fully bought in to this system, then you and other supervisees probably cannot dislodge or change the system (as it is too entrenched). Usually, on a company-wide crisis can disrupt it e.g., mass exodus of the unrecognized, high talent, underpaid folks who actually do most of the work; or exodus of people with intmate knowledge about critical, long term cases or who have info about legal and ethical violations at the company. What I generally recommend is that individuals in 'like circumstance' in this company consider launching into their own firm or business, or finding a different company to work for, cut back to part time and take on teaching positions at a local/regional law school as an adjunct etc. Entrenched problems can be to monstrous to change on one's own and trying to tackle them alone or as a "Don Quixote" will bring on more stress
and personal, professional damage.
It is best to plan-fully and very privately hunt for other options with another firm, or start one's own business. This is easier for the truly underpaid, underappreciated talent at a firm because they have certainly nurtured lots of good contacts, clients etc., over the years who really 'love them' and might jump ship to give them business if they start their own company. So a big part of whether this suggestion might be successful on not is highly contingent upon how good you really are at what you do. Let me hear your thoughts and reactions to this