@Nicol.Bolas That's basically my experience - I never put GG units in harm's way. They only fight at 95% or higher, so a 3-promo unit could have reasonably won the fight at 80% odds or so.
But all this misses the larger point: Wars are about siege. If you're doing it right, siege damages everything to 25%-50% health, then the regular units just clean up in fairly easy fights. The only time you need a strong attacker is if your siege didn't do it's job (meaning the enemy unit still has close to full HP).
(For more on why siege is necessary, see the stack o doom guide: http://forums.civfanatics.com/showthread.php?t=185838 )
Siege units are there to die, so you can't put a GG on them. The only way to help siege is to settle the GG. And once you have good siege, ordinary 3-promo units can mop up easily.
(This is the same reason Charismatic is better than Aggressive - wars are about siege, not melee. See http://forums.civfanatics.com/showpost.php?p=8824380&postcount=106 ).
Welcome to the forums!

Like you, I don't put my GG units in harms way. Of course, my only GG units are supermedics, everything else gets settled.
Note: I think the Military Academy question is partially decided by what speed you play on. Normal it might not be worth it if you can get out units in 1 or 2 turns. On Epic or Marathon then the Military Academy becomes more attractive.