Why doesn't the VA send my prescriptions to a military facility, where there is no cost to me?

Money. The VA and DOD are two independently funded agencies. Your copay at the VA was imposed to have veterans pay a portion of the cost of their care based upon the percentage of their maladies attributable to their service. Your copay reduces the operational funding congress must allocate to the VA. Even if the VA provided your medicine to DOD free of charge, the DOD would have to fund any additional personnel required to handle processing and distribution of your medication. If the DOD was authorized to bill the VA for services and material provided to vets, both agencies would have to increase manning to accomplish the costs of funding the distribution. Two different agencies with different missions and neither is going to allocate any of their funding to accomplish the other's mission/responsibility.

PFC Mosier's reference also includes many situations that can be used to excuse the copay if it is a real fiscal burden.

That’s a good question to ask but that’s a conversation to be had by two different Hospitals working in two different coverage networks. It’s not something that would happen automatic.

If you are over 50%, I think they ship them to your home free.