The humans in Star Fleet must be some kind of future mutation due to the fact that Deanna Troi doesn’t feel constantly sexually harassed.
Regular port calls to Planet Ologngopo for Pon Farr.
She was such an obvious tease (flashing her boobs and then using psycho-BS to put you in your place) I doubt many men thought she was worth the effort.
They tried stripping down a starship to just the crew and equipment needed to fight in battle: the result was the Defiant.
To be fair, the Enterprise was never intended to be a purely military vessel. In a galaxy in which deep space exploration can and has resulted in running into some very bad things, a ship venturing into the unknown has to be well-armed just to survive. It has to have scientific facilities to analyze the strange new stuff they run across, it has to be a diplomatic envoy for first contacts, it even has to haul supplies to remote outposts on occasion. There really isn’t that good a terrestrial analogy since Europeans developed cannon-armed global range ships before anyone else, and never faced any serious opponents at sea except other Europeans.
I thought that Starfleet was intended more as a kind of 24th-century Merchant Marine, whose goal is to explore rather than facilitate trade. They’re not supposed to be the Federation’s police force, even if they frequently end up acting like it. I thought GR was pretty adamant that Starfleet is not the US Navy in space.
As the flagship of the fleet, it wouldn’t go anywhere alone. How many times were capital ships in the Star Trek universe basically screwed because there wasn’t another ship nearby to offer help? Particularly when they ran into Romulans or Klingons, and they would always have at least three ships.
The closest analogy is the British Royal Navy of the 18th and 19th centuries. Starfleet’s primary purpose is exploration, scientific research, and seeking out and contacting (where appropriate) hitherto unknown life and civilizations. Regulation of commerce, diplomatic missions, providing protection to Earth colonies, performing police actions, and even waging war are all secondary functions.
If you can find a copy of The Making of Star Trek (mine is lying around here … somewhere), you’ll see where all this is spelled out in the original series format.
The uniforms would incorporate name badges and multiple and highly visible rank insignia.
The ship’s chief therapist would not be a bridge officer.
Shipboard recreational facilities would not be capable of creating sapient AI constructs with access to deadly weapons or the ability to override the ship’s computers.
Any time a human says “shields up” or “raise shields”, the AI would respond “the shields were automatically raised the nanosecond a vessel or body was detected within 100 kilometers of our location”.
God wouldn’t need it.
Even 100,000 km would be too close. 100 km is spitting distance astronomically.
Touche.
They have the Holodeck to take care of all such needs.
The original Galactica didn’t do shit to defend itself until the Cylons were within microns.
Starfleet serves the Federation in three capacities: Exploration, Scientific Research and Militarily. All three are equally important. Since it’s an action show, we tend to spend most of our time watching the adventures that focus on the latter.
The Royal Navy did a lot of that in its heyday. Even today the US Navy has a pretty big scientific effort.
As it is, the we are not military is bullshit. When the Dominion comes calling, who does the Federation turn to? Starfleet.
“I have never subscribed to the theory that political power flows from the barrel of a gun.”
Captain Jean-Luc Picard, Captain USS Enterprise (NCC-1701-D)
Star Fleet flagship
Ship Armament and Defenses:
12 Type X Phaser arrays
3 Torpedo launchers
Antimatter mines
Deflector shield
Various armed shuttlecraft
Crew of approximately 1,000, including Star Fleet security forces and other personnel armed with various phasers
In the RN of Nelsons period, it wasn’t uncommon for the Captain’s wife to sail along.
Sure, look at the Voyage of the Beagle, or Captain Cook’s missions.
Of course, with all of that, Picard’s default defense was diplomacy. 
Tiger cruise.