My mind immediately went towards Battlebots when I saw electronics getting involved. I wonder what else would need to be done to make this steerable over RC? There may be a lower weight class where some nicely CNC'ed 'Phantasm Orbs' can score reasonable points.

This already exists- there's a class of robot called "meltybrains" which spin the whole robot using one or more wheel, detect the speed of spinning with a gyro and modulate the speed of the wheels at different points in its' rotation in order to create translational movement. Since they effectively put all the weight allowance into the "weapon" they can be very effective. The additional complexity means that they are hard to get working reliably in chaotic combat conditions. A team called "Project liftoff" had some serious success though.