I have always failed to understand the obsessive dream of many engineers to become managers. It seems not to have to do merely with an increase in revenue. Is it really to escape from "getting bogged down in the specifics" and being able to "focus on the higher-level, abstract work", to quote OP's words? I thought naively that engineering always has been about dealing with the specifics and the joy of problem solving…
I think it's that there is only that much demand for solving really complex problems, and doing the same thing over and over is boring, so management is the only way forward for many people