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.

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 Neil stated, there is no need to remeasure your alignment features.

it is best practice to try and measure as much as possible with the one tip before indexing or changing tip angles.

if you are worried about the indexing repeatability, perform an auto calibrate after each tip/index change. This is more important if you are using long extensions and are measuring parts with tight tolerances.

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.

0.0005"=0.013mm, How about calibration from 9 hits to 18 hits? How much accurate It could improve?