In my opinion, it would greatly improve the game immersion if the weapons were only draw during "red-alert" (combat) situations on the ground. You could still draw by pressing H, but they would be, by default, holstered in non-combat situations.
That would prevent players from running in public places with weapons on their hands by default. I think it is quite disturbing to see dozens of starfleet officers running in an Admiral's office carrying all sorts of heavy weapons.
Just my two cents
Whoever reads this and agrees with me, please do say so to get their attention