To be honest, I wish a requirement for President was that you served in the military. Why should the President be Commander in Chief and not know a thing about the military. It does not make sense to me that someone who never served be President.
I don’t know, but I would think that the framers expected many would serve in State militias ergo service for a lot would be included.
However, except for the obvious exclusion of women & blacks, they seemed to be more interested in letting more participate rather than less (not requirement for owning property, having a peerage, etc.)