Can FOC be done with only one PID controller and a lookup-table that determines phase-offset?
What you are proposing is an open loop system, which works if the sensors are highly accurate and there is little drift in the system. Theoretically it there would be little or no difference during steady state operation. However during transients, i.e. sudden changes in torque and speed, you would likely get sub-optimal performance.
What an open loop system cannot compensate for is drift, e.g. due to temperature change. For example, as the windings were to heat up, or the mechanical bearings were to develop more friction after hours of running, the characteristics of the motor will change slightly. When this happens, your open loop system will no longer be as accurate.