I think that it is VERY helpful if the president knows what they're doing and has been in the military, but if they know what they're doing, I don't believe they should have to be in it. Basically, know what you're doing, don't form a dark alliance with Satan, and KEEP A GOOD MILITARY. Seriously though, the War of 1812 happened in part because the American military was cut down.
This actually is not a very good idea at all.
First of all, in 1812, Imperialistic nations were rampant and the British were still sore over the lose of America. We live in a new day and age, and the UN law states against wars of conquering, so regardless of the condition of the US army no recognized state would be allowed to declare war on them unless we did it to provoke them.
The only group we are 'at war' with is terrorists, who are not recognized by the UN, and we could reduce our army by 100-fold and such a small group would not be able to even consider launching a full on attack. They operate by stealth and surprise bombings as the US military vastly overpowers them.
Furthermore, we are entering a new day and age. People seem to think that WWIII is on the way, and we all need to prepare for the apocalypse, but think. Seriously, THINK. WWI, and WWII both had HUGE underlying causes. WWI started a result of Imperialism, which started as a result of the world discovering itself. This was a one time process that likely will not happen until we colonize space. Furthermore, WWII started as a result of the conditions that WWI left the world in.
Well, I feel that if the president had military experience, he might turn out to be a blood thirsty war-monger and plunge us into WWIII or something. Just a fear.
To both of you, I would like to stress that the odds of WWIII happening ANYTIME in the next, at least hundred years is remarkably unlikely. I could go into more detail, and raise more facts but I must leave. I will be back in a couple hours.
EDIT: I realized I formatted awkwardly, my content support for this claim ^ is above the 'reply' I replied to.