Would it be beneficial to have rotors AND propellers instead of a tiltrotor?
There are 2 major problems. First is the weight you'd incur from:

Extra rotors/propellers
Transmission components (the V22 already has a transmission in case of an engine failure, it's already more complex than you'd ideally want but it's necessary for safety)
Structural components to support the forces from the propellers and extra transmission

It's lighter to turn the engine and rotor together, and probably more reliable.
More importantly the rotors have aerodyamic issues at higher speeds. Remember the rotors are still up there, and they must be dealt with. You could:

Fold them away or back: you'd need a mechanism capable of stowing and unfolding the rotors in an airstream, which means weight
Have them produce no lift: this means they will be dead weight so they will take away from payload
Use them for lift: this would be similar to a gyrocopter, where a rotor is unpowered but produces lift from forward flight. There's aerodynamic limitations due to the differences in lift from advancing and retreating blades which would limit your top speed