This is absolutely not a feature, it's a bug and should be addressed as such. It's unrealistic, counter-intuitive and slightly game-breaking. As Good Stuff and Sastron pointed out, it's very useful or even necessary in situations where you need to move really fast, especially to evade an attack, like the Giga Slime's. Speaking of the Giga Slime, it moves as fast as you do going straight, but not as fast as you do diagonally. This doesn't only feel awkward, it also greatly influences your options in some situations. If players feel the additional mobility is important, you'll have to either adjust the speed of such enemies downwards or increase single-axis run speed (or maybe implement more mobility skills), but it's unavoidable to adjust the diagonal speed correctly, otherwise you'll run the risk of such attacks as the Giga Slime's (and, to a lesser degree, every enemy, considering that they all move at the same speed in every direction) being unbalanced - easy to evade if you can run diagonally, but hard/impossible to evade if you can't.
On a somewhat related note, I'm wondering if you ever intend to enable omni-directional movement for joystick/controller users. This seems logical, considering that enemies have it, but then again, this would somewhat favour those players over keyboard users.