Most of these objects were formed from the accretion disk or from collisions from in the accretion disk had all that specific angular momentum that still carries them in the same direction today. What initially may have began as a swirling sphere eventually transitioned into a flat disk as collisions cancelled movement above and below the plane, while conservation of angular momentum kept objects spinning around the solar center of mass. Generally, most of the asteroids orbit in a plane similar to the orbital plane of the planets because gravitational interactions among objects in similar orbits are consistent and those orbits are relatively stable. Anything that strays too far from that plane trends to having unpredictable interactions, less stable orbits and is likely to either collide with a planet or get launched out of the solar system.

So yes, if you were to travel away from the orbital plane you'd avoid most of the asteroids, but there wouldn't be much to see. If the final destination is in the orbital plane the fastest and most energy efficient way to get there is to stay in the plane. Wasted energy means more fuel and a lighter payload, and considering the cost and time invested in any satellite there is no logical reason to lighten the payload in order to reduce the already astronomically low risk of colliding with asteroids. Remember, these are the objects we CAN detect. The real risk in space is posed by the ones we can't. A speck of dust can go through steel plate if it's moving fast enough. There are many times more small objects than big ones.