It does seem historical inaccurate that you train a specific unit type. Historical the senate would of raised a legion not recruit three units of hastari (ignore spelling). So would it not be better if instead of training individual units you instead would raise a legion or something. Yes it would take more than one turn to create but it would consist of several different roman units ie hastair prinnipier, like a small army.

You could implement the same thing with a barbarian faction ie call to arms or something.