Endeavor is convinced that having a freezing/fire quirk would make you stronger than having a fire only, to the point he had several children to get one who displays such quirk. But at first impression it doesnt seem to be obvious than having both options would make you stronger than having only one. Does he ever mentioned any reasons to think so? Which reasons does Endeavor have to think having a freezing/fire quirk would make you stronger than having a fire only quirk?
Just having one of freezing/fire quirk has a major weakness. Your own body is not immune to the effects of your quirk. We see this in the sports festival when Todoroki's body starts to freeze because he wasn't using his fire quirk.
We also see the same thing much later in the manga when Endeavor's body gets too hot while fighting the new and stronger Noumu.
Endeavor has always been aware of his weakness and knows what the solution is. If someone had both fire and freezing powers, then he could reverse the adverse affects on himself. This is what Todoroki did at the end of his fight with Deku.