I would speak to whoever your direct supervisor is and ask to learn about how the company manages project of this size. Maybe point you towards any documentation in the SDLC. Clearly you don't understand what the program manager is doing. If they are traditional PMI type program manager, than they exist because what you are doing is called a program, not a project, wherein there are multiple projects that make up the program.
A program manager with multiple projects running concurrently is going to be trying to determine how many project managers there needs to be. Given that traditional programs have multiple deadlines, might have multiple development teams, qa teams, deployment teams, and a wide range of stakeholders, you may be underestimating what is necessary for the project management side of things. A program manager who underestimates what they need is failing. A project manager who underestimates what they need is failing. As a developer, you give estimates and the project managers try to understand how to use those estimates to determine resource needs. As a project manager, you have to include not just development work, but project management itself. Project managers who are programmers tend to try to close gaps by programming rather than project managing. The program manager doesn't have any recourse there. They can't dive into detail level. Its actually important that they don't. A project manager should be helping identify tasks, so that they can prioritize work based on dependencies. They need to be able to continually communicate resource gaps. A program manager should be taking oversight over multiple projects.
So basically if this project is simple enough that a single person can manage the teams necessary, with all communication being handled in a timely way, change control, qa, and deployment teams all easy to manage, then sure, smallest team necessary is best.
But if the issue here is that you just don't like the culture of enterprise development software development life cycle, then you are in the wrong company based on what you describe.
Having spent a lot of time running a small fast software company and a freelance programmer, and 5 years watching a small company get absorbed into a large company, I know a lot about how this works. Personally I am a better project manager than most people I know, but I hate it and since i am also a better design/architect/programmer, my bosses agree to try not to make me project manage. That being said, because the very large corporation I work for is extremely resource tight, and believed in flattening their management, we have very few project managers and we have suffered a lot. If your company has drank the ITIL/PMI coolaid and are willing to actually allocate the right qualified team members to fill those roles, than you are very lucky. Mostly I have seen companies whose leadership is trying to enforce those things, and doesn't invest in the necessary resources to make it work (so that too few lead chefs mean everyone has to do work they aren't good at)
Before you assume that your MBA type program manager sucks, consider that good project/program manager is a skill independent of the goal. A good project manager can figure out how to get you to the moon without knowing anything about aerodynamics. If you can learn a bit of that, then at worst you may be better at communicating to project managers and the people who hire them, and you may even be better at hiring project managers in the future.
If you treat it as a case where the guy is not valuable because his knowledge isn't based on software development skills, well I have news for you. None of the expert programmers I know can project manage worth a damn. Guys with 30 years of experience don't know how to think about projects in a way that is constructive. They may be problem solvers in their domain, but project management is its own puzzle. If you don't respect it, then don't expect to work well in the modern offshore heavy, PMI/ITIL driven enterprise world.
So yeah, if all you are making is broth, then too many cooks is bad.
I assume you want to do something a little bigger than broth in your life.