Redo alignment after tip rotation?

If you are chasing sub 0.0005" tolerances, re-measuring datums after a probe rotation will mitigate any additional variation caused by probe angle/calibration changes. 
--So it really depends on what kind of reproducibility/accuracy you are needing to quantify.   IMHO if you have 0.005" tolerances, yes it's a complete waste of time.

As louisd  stated, it depends on my tolerances for the features that I will be measuring and in most instances I will not remeasure datum features. I have hole position callouts on some parts that are a low as Ø 0.015mm on some surgical instruments and for this I am using a star probe and before I measure the hole I will touch off on the 2 datum surfaces (Y and Z) with the 90° styli that I be measuring the holes with.

As louisd  stated, it depends on my tolerances for the features that I will be measuring and in most instances I will not remeasure datum features. I have hole position callouts on some parts that are a low as Ø 0.015mm on some surgical instruments and for this I am using a star probe and before I measure the hole I will touch off on the 2 datum surfaces (Y and Z) with the 90° styli that I be measuring the holes with.