To quote Voltaire: “
Give me the child for the first seven years and I will give you the man.”
Yeah, Tommen being loyal to the Tyrells but capable of ruling and acting in his own capacity is very much the best case scenario for the Tyrells.
There’s also the fact that the Tyrells aren’t just pure, naked power politics actors. They probably feel a certain level of responsibility towards the boy they’ve pledged their house to, especially given his mothers manifest unfitness. They’re capable of expressing genuine concern for his education and having affection and empathy towards him, while at the same time seeking to secure their own political advantage and future.
It’s the very definition of enlightened self-interest: the boy in question is Margaery’s husband and (if they get their way) the father of her children. Moreover, the Tyrells had to assassinate the last boy king that they hitched their wagon to because he was unstable and a threat to Margaery.
Putting some basic effort into educating and loving a child who is neglected and despised by his mother is the very definition of a win-win: it raises the chances of a capable monarch and loving husband, it advances the Tyrells’ influence vs. his mother, and so forth.
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