There's something called "cost", though, and a bolt is pretty useless without a good directed spell bonus. Cost-wise, the warrior-mage has a 3/6 for directed spell and 2/7 for his primary weapon. To be efficient in all the elements and have some weapon skills, a warrior-mage would need 9x5 + 9 = 54 dev. points... for the skill ranks alone!
So, yeah, a warrior-mage never gets to fully develop most of his elemental bolts anyway, thus never allowing him to be the so powerful character people think he could be.
For my part, as a GM, I stopped making and advising to my players warrior-mages because they have always proven to be quite useless because of their very high skill cost for just about everything.