Perhaps concerns about 'the over-militarization of police' is essentially a concern for situations where an extreme power imbalance exists between police and civilians, creating a much higher risk of totalitarian abuse and oppression by police in situations where the police force in question becomes corrupt or 'bad' in some way. (Disclaimer: I'm not making an anti-LEO argument; quite the contrary, I'm very pro-LEO, and in many cases I see, LEOs are disrespected very unfairly.)

The problem isn't where police are good; the point is to design a system that inherently protects against abuse by the very small percentage of LEOs that do become corrupt and abuse their special powers that civilians do not have. How do we protect against this?

Perhaps the simplest and most robust way to protect against this abuse is simply to limit the magnitude of power imbalance between the government and the people! One could argue that this principle applies to physically defensive equipment as much as it does to computer and information systems, and any other mode of power. Additionally, this notion is encoded into our country's constitution at least in some ways.

Therefore, this leads to the question: Can a civilian buy an MRAP? If so, I think your argument works very well -- especially since they're defensive machines. If a civilian cannot buy one though, I could see the argument against police using them gaining favor.