Lol. It's already what's happening.
I totally back this suggestion, yet I read somewhere that these training grounds should have a max level a unit can get.
Like max tier 3, so a peasant can become kind of a soldier thanks to training, but cannot become a war veteran without actually surviving any.
This I like. But I also think there should be places available, either in arena, a castle, or somewhere, where you can pay to train any troop, or high end troops, for the right sum. I have played and am playing right now with Xorberax training fields which implements this and I think it's been a very nice addition.