What benefit would that test provide?While the Ship has flown and landed, the booster has never flown.
Perhaps it might have been wise to test the booster by flying it the same distance as the Ship and try landing it by catching on the chopsticks.
Having an unproven booster purposely operating around Stage Zero more than necessary seems risk heavy.
Requirements:
Get Starship to 64km with appropriate velocity
Separate and spin
Relight for boostback
Survive re-entry
Relight for landing
Control both its position and zero velocity point
Once all those are achieved, then move the 0,0 point to the chopsticks.