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
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Have you noticed how little crime occurs on starbases now? Thank your starfleet officer today!
Would you like to know more?
imo it should be enough to seperate between hostile and not so hostile environmenty
eg planets and (certain) starbases
That's another idea.
But honestly i abhor walking around waving a gun. Taking a cue from EVE's future Incarna update, STO should invest in immersion by taking a close look at small details.
In a starfleet starbase people don't:
Run
Walk as robots
Wave guns around
Jump around
Jump on tables
Push others around
No flames please this post was meant for humor purposes only. Thank you come again.