I do not shoot double rifles. That said, when both chambers are loaded and the first round is fired the remaining round is buffeted by the recoil and this COULD result in the entire cartridge moving slightly forward (through inertia) or the heavy bullet moving rearward in the cartridge neck.
I DO crimp all rifle rounds from .25 caliber up. I definitely think that crimping (with the Lee FCD) makes a better round and helps to maintain even neck tension, which positively effects precision.
When using the Lee FCD you do not need to 'crush' down the press lever. In fact it does not take much downward pressure - maybe 3 to 5 lbs. for most calibers. Try to be consistent.
Crimping is easy, cheap and helps avoid potential problems in the field.
To that point, I learned something from @Wahoo (he's having a great safari as I write this) about the crimping considerations. He tried literally every 470NE and 375HH bullet known to man because he's that kinda guy. He was looking at SAAMI/CIP specs and then testing them for feed function in his rifles. What he found on more than a few of both calibers is that the cannelures or driving bands do not line-up within the required Over All Length (COAL) to be within spec. That is a pretty good reason for a factory crimp die, because you may not be gripping a cannelure and you'll appreciate that extra neck tension in that case especially.