I think thats kind of a facile argument, in both directions.
First of all, while I do agree that the military does provide an actual service to the country, I do feel that it is way bigger than it needs to be. The same security benefit could easily be achieved with a smaller military.
Second of all, social services do actually provide an effective service to the country. Especially where programs such as primary education or health care are considered.
Considering the amount of actual defending the Department of Defense does, I'd say it's more of a luxury item to some extent. Force projection across the globe was not what the founding fathers had in mind.
We spend more on everything than any other country, because we have the money to burn, and as you've said we also seem to have the money to waste.
But, that aside, I don't think government waste is really a good pillar of a concept to defund education. I think you're on the right track with removing waste, lets stick to that, rather than gutting critical programs.
Seemed to work for Toyota.