This is one of the more contentious issues that always sparks a multi-page thread. Briefly:

Campagnolo specifically states to assemble their square taper cranks dry with no grease at all on the spindle. They give no reason for their recommendation.

Shimano doesn't say either way for their square taper cranks. They do specifically recommend greasing their Octalink spindles but that's a completely different interface.

The bicycle -savvy mechanical engineers I've seen weigh in on this issue say these tapers should always be greased and I tend to follow their recommendations. I grease the spindles and have never had a problem with any square taper crank (Shimano, Campy, SR, Sun Tour, etc.) loosening or distorting in 25 years of working on bikes.

One caveat, when you install the crank arms, torque them to the manufacturer's spec and then leave them alone. Some riders "check" the arms and will retorque them numerous times, often after every few rides. Doing this will indeed force the crank further up the spindle and lead to eventual failure if done enough.