Why would an organization like the DoD prefer to use its own Root Certificate(s)?

They do rely on generally available CA root certs for sites that are expected to be generally avaiable to the public over HTTPS. See https://www.army.mil for one prominent example.

However, the DoD has a significant internal CA infrastructure and they perfer to leverage that instead for sites that either aren't intended to be served over HTTPS at all (like your https://mrmc.amedd.army.mil/ example, where HTTPS requests are simply 30x'ed back to http) or sites that are designed for internal use by folks on DoD equipment like http://www.dau.mil (which requires a CAC [DoD-issued smartcard] for authentication as well) or http://www.forge.mil/.