In general, in my opinion, a well-rounded hero is better, one who is proficient in both combat skills and magic. Yes, it's not always possible, but with different "upgrades" on the map and using different artifacts, you can still get such a hero! But I absolutely cannot stand a hero without magic or a mage who can't "hold a sword"!
By the way, who has played (and won) on the map "Heroes of the Sword, but not of Magic," where magic is practically excluded? There, of course, brute force decides everything (Crack Hack "in the hands" of the computer is a terrible thing!). But, as it turns out, even a warrior hero really needs magic in battle!
As for mages, even the coolest ones still need an army!
And battle mages are called that because of their initial characteristics: 2-1-1-1, which is much more useful in the early stages of a hero's development than for other mages, who have an attack and defense of 1 or even 0!