Regarding multi-use, I, for one, wouldn't want to command a crew that had sidearm/tricorder/communicators somewhere on their persons at all times -- especially since, in TOS at least, landing parties are so often separated from their communicators.
Having a separate gun from your "phone" and sensor device makes sense. If you're firing it extended at arm's length from your body for accurate aiming purposes, then having to yell at something near three feet away in a combat situation would be impractical.
And in a diplomatic or casual environment, if you had to go to what everyone in the room knew was your gun to call the ship, this could be socially unacceptible.
Hopefully there is gun control in the 23rd and 24th centuries.
Hopefully not. The future should at minimum have as many freedoms as we have now, and preferably more. But certainly not less.