Or as one of my colleagues so aptly put it, "SWEs are not fungible."
For some reasons, PM are thought to have a great understanding of both functionals and technicals of a solution, while at best, the only good they are at is navigating the organization and shielding the team.
So in a word, management is most likely useless and PM even more, especially if the management believes that a PM can handle a few projects at a time for cost saving (!).
I know you are venting, and even agreeing with me, but I wasn't trying to make this a SWE vs PM thing. The dynamic you describe hasn't been my experience, at least so far.
Wherever you work, I hope you find ways show the value of your work to your management chain too.