what is the purpose of trainer heroes?
They give more xp when used to level other heroes. So their purpose is what the name says , train other heroes 
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So, are they only meant for leveling? What if you made a team comprising only trainer heroes? Is that team useful, or even advantageous/required?
No, they have low stats and a weak special.
They are only useful as a last resort for new players.
They have no class or family bonus.
The only time trainers were widely used was the 2* tournament which happened once and then got cancelled!