To avoid placing a secondary mirror in front of the objective mirror, why not tilt the objective and design the eyepiece in such a way that comatic aberration is minimized?
Aberrations. A parabolic mirror perfectly focuses rays along the optic-axis, while off axis rays are blurred--tilt the mirror and you get more light, but it's out of focus. I would guess that the non-tilted mirror has 2nd order aberrations, while tilted one is 1st order: it's a lot worse.
You can't just tilt the mirror (for the reasons described in JEB's answer).
You can have off-axis parabolic mirrors but they are tricky to make. You either have to machine the surface with a diamond tip CNC machine, or saw an off axis region out of a larger mirror
At radio frequencies they are a lot more common. Where you can make the shape from metal plates.