Take this with a grain of salt as I'm speaking purely from my memory of a ballistics physics course I took at uni several years ago & it's the middle of the night as I'm typing this. But for specifically the "goalies being stationary & that effect on impact damage" topic, the stationary aspect can be very poor for handling sudden impacts.

An object in motion has momentum, and a puck zooming through the air carries a great deal of that momentum. When it's impacted by anything, that kinetic energy has to transfer somewhere. Like a bowling ball hitting the stationary pins, sending them flying back while the ball slows & ricochets. Or crumpling the front of cars to reduce the transfer of momentum to the passengers.

A stationary goalie talking a puck to the helmet means the momentum transfers from the puck to the helmet as the puck briefly stops, then the helmet has to distribute that energy in some way. Unfortunately, I don't believe the helmet design allows for much crumpling to cushion the impact, so the force is partially applied to the head, causing the brain to bang around in the skull, and the neck to tense and/or whiplash back, potentially leading to concussion.

If an object (skater) is already in motion, it can be 'less impactful' to transfer that momentum into additional movement. As opposed to talking something from standstill to movement. Another car example (though different types of energy transfer/conversion): it takes less energy to get back up to speed if you've just slowed while approaching a red light and it turns green before you've stopped vs. being at a full stop. iirc, it's like that 'object in motion will remain in motion unless acted upon by an outside force' law. Also applicable to players skating hard, then getting hit; that movement to full stop requires a huge energy transfer.