I personally don't think that grease or no grease is of a major significance.

I DO think that maybe folks are forgetting the re-installation (CLOCKING) of the square taper (spindle to crank arm) to be of greater importance.

Manufacturing tolerances and the previous (as removed) taper set / relationship should be observed (witness marked) and re-installed in the same relationship IMO. One has a potential choice of four different reassembly positions. Reassembly to the original relationship would offer the optimum (factory) alignment with regard to taper-on-shaft advancement, chain ring radial and axial trueness and chain / DR alignment. No?

I don't profess to be a bike mechanic Guru, but my many years of Naval Engineering, Automotive expertise and Machinist training, guide my thoughts here. I also happen to have recently rebuilt the crank on my ST with the same components as the OP.