It may even be more rigid than what is there now (though nowhere near rigid enough to do anything real)
The design is actually not unique at all - you can buy much better versions of it (at higher cost, obviously).
Most positioning actuators you can buy are literally built to be attached to each other in a cross-slide configuration, and to have a rotary table attached to it. They also directly sell pre-built cross-slide actuators.
If you just google "cross-slide stepper" or "cross-slide servo", you can see this (servo/stepper just gets rid of the manual ones, which also exist).
The normal reason the configuration is not used is because it has no meaningful rigidity.