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Everyone fights with their imbue activated which utilizes the magical damage of the weapon. So, wouldn't it make sense to go int rather than str?
No, because one of the main bow skills relies on crit, and an int's crits don't hurt at all. As int bow, you lack the extra defense that a sword/shield will give you. Also, you lack the power of spear skills. So basically, you can think of an int bow as a much weaker int spear: w/o the defense of a shield and w/o the power of spear skills.
An extra percent of int will actually give you more magic damage, but not significant enough to make it worth it. You could be using those str points to allow your crits to hit harder.