Just wanted to point out that typically in the US, the role you seem to be describing is that of an engineering manager, not a project manager. If your company is finding engineering managers in 2-4 weeks, it probably is not a top-tier tech company.

At the highest paying tech companies (FANG) there are usually 3 "manager" roles:

- Product Manager: Interfaces between marketing, engineering and design to manage the development of new features and products. Not necessarily a people manager and does not directly manager engineers.

- Project Manager: Manages scheduling, task assignment, communication between teams, assigns bugs. Does not directly manage engineers.

- Engineering Manager: Primarily a people manager, usually was a SWE previously. Does manage engineers.

Of the 3, the project manager path is probably the least lucrative at the same level. Product and engineering tend to have similar pay.

Good engineering managers have a unique blend of managerial skill AND technical skill. On the other hand, there are lots of anti-social weirdos that are great ICs in engineering. As a result, I'm inclined to say that supply and demand is working pretty well.