You are forgetting the ‘cursa honorum’ which was a career ladder for young Roman nobles to become Senators and politicians.
The cursus honorum began with ten years of military duty in the Roman cavalry (the equites) or in the staff of a general who was a relative or a friend of the family. The ten years of service were intended to be mandatory in order to qualify for political office, but in practice, the rule was not always rigidly applied.
A more prestigious position was that of a military tribune. In the early Roman Republic, 24 men at the age of around 20 were elected by the Tribal Assembly to serve as a commander in the legions, with six tribunes to each and command rotating among them. Tribunes could also be appointed by the consuls or by military commanders in the field as necessary. After the reforms of Gaius Marius in 107 BC, the six tribunes acted as staff officers for the legionary Legatus and were appointed tasks and command of units of troops whenever the need arose.
So most accomplished politicians in the Republic had quite a bit of military service with the legions as part of their training and qulaification for higher office.
Wouldn’t it be nice if we had the same sort of requirements? I think we are down to only a few Senators with military service (Kerry, McCain, and the guy from VA.), probably the fewest in our history.
Not forgetting the military prerequisite for the cursus honorum. I thougth about including it in my post, but didn’t want to overly complicate the discussion.
As I understand it, in theory 10 years or 10 separate campaigns of military service were required. I am unaware of any requirement this had to be in the cavalry, and I believe most young aristocrats served in the contubernium of a general, essentially on his staff, as you say. The young J. Caesar, as a non-typical example (there wasn’t anything typical about him), served his 10 campaigns all over the Med, in a wide variety of positions.
I wouldn’t have a problem with a military service requirement for political office in this country.