Dear Selena, you are wrong in many ways: a Barbarian mage with your build can easily defeat them without any particular problems, so a pure mage is not very effective.
I agree, magic doesn't solve everything... combat skills are also important, even for mages. Otherwise, you'll have an army with its inherent stats...
And it's not necessary to max out all magic skills; a couple of schools are enough (considering who you're playing as and who you're playing against), and I doubt you'll need all the spells in a battle...