I gotta say… a lot of these proposals sound like good shows. They don’t sound much like Trek, though.
I would like a show that’s set on a Klingon or Romulan ship, and not Yet Another Starfleet Ship.
The best shows involve a core group meeting different challenges each week, with no fake “get off the island” dilemmas - in other word TOS and TNG. I’ve been working through all of TNG, and have just watched a show where Picard’s reaction to the display of godlike powers is “we can do all that stuff.” So how about a show set 50 or 100 years after TNG where their technology has gotten ahead of their moral judgment. If humans are headed to Q-ville how do they deal with all that power. It can begin with the breakdown of the Prime Directive as they realize officially that not interfering with a culture about to die is not necessarily moral.
While we’re at it, we can have Spock go to the Guardian of Forever and go back to fix his mistake to cut off the Abrams timeline entirely.
This would be a win. Especially as it becomes clear over time that the antagonists are the ones in the right.
I want a Star Trek with some really alien aliens, not just humans with skin conditions. I want their actions and motivations to be unfathomable and dangerous, and for humans to be rather afraid of them because they can’t reliably communicate with them.
I want one that harkens back to the adventure and action of the original with the special effects of today. Much like the Doctor Who revival that is so well done. The Original show for all its 60s themes and cheesy by today special effects was the most action oriented. I loved the space battles we got and the fact they welded a really strong power trio in the original. Keep down the angst at all cost.
Star Trek: Corsair
Due to a crisis of conscience, a Federation officer goes rogue. He/she liberates a select group of prisoners, steals a ship, and travels through space as a pirate. Now, in addition to all the traditional villains, he/she has to evade the forces of the Federation.
It could work!
That might work into the Maquis theme.
They sorta did this a la Blake’s Seven.
A good point. Let’s scrap the crisis of conscience and make the protagonist a real rogue–an Errol Flynn type who gets arrested after disrupting a political wedding. The Federation puts him in prison, but he breaks out with a squad of desperate criminals, each with a mysterious past.
The Federation will still be a bastion of liberty and political correctness. But will they catch this pirate? Or will he mold his unruly group into an effective crew? Find out on…
Star Trek: Corsair
Unfortunately it would be competing against Star Wars: Buccaneer, and Stargate: Scoundrel.
How about an investigative/diplomatic Star Trek Federation unit.
A unit sent out to investigate or negotiate possible new federation members. They would need to visit planets to determine if the people of a specific planet qualifies to join the federation.
In each episode, you would encounter specific issues or problems which could be an issue for membership and you never know if said planet qualifies.
In addition, the group would also be responsible to investigate current members when and if a situation occurs where they may be breaking federation rules and could be expelled if violation is too severe.
They would also be responsible for first contact missions once a planets population has reached a certain level of technical advancement.
Finally they are also responsible to investigate possible violations of the prime directive.
The only problem with this that I can think of is coming up with a major foe. Perhaps Romulans, Cardassians, Breen or even Ferengi could be foes competing for planets.
On a side note, the crew would have frequent inspections to Risa of course.
Oh! I got it! It could be a new foe early on, let’s say in a first contact mission where it turns out they encounter a very xenophobic race who have developed warp drive. What was unknown is how advanced their weapons are and they become a seriously dangerous foe who quickly expand their territory to rival the federation.
**NCIS: StarFleet
JAG: TNG
DS Alcatraz**
Sure, we have replicators, uplifting goals and ideals, socialised healthcare, and lots of pretty women in tight outfits. But, we can’t evolve THAT much in a few hundred years, not like Gene was thinking anyways. We still are going to have murders, drug addictions, family strife, etc … (as seen in a few eps of the various series).
I honestly think this has been the single best idea for a Star Trek series thus far. I might expand the premise a bit more, maybe they also do solve problems that arise between Federation members, just for example, but I think you’ve got a rock solid idea.
One from me, awhile back…
Another post-Dominion War idea: ST-Detente. The new, and uneasy, allies the Federation and the Romulan Empire develop a joint mission to explore the Gamma Quadrant. Culture clashes, multi-layer plots, and other frictions ensue - and that’s just among the crew. You still have the “wagon train in space” aspect, and chances for ship-to-ship action and conflict, as well as chances for diplomacy.
Is Tom Stoppard available to write it?
The Groaci of course. 
“To put your phaser down, Starfleet Diplomat.”
Actually, I like this idea, since the discovery of an interstellar culture is more disruptive than ever seen on Trek. What does it do to the native religion and science?
Plus, one of the good things about TOS was its political commentary - heavy handed at times, but at other times quite good. We can see cultures illuminating some of the trends in our present-day culture, and look at the issues of changing to the Federation culture - if this is even a good idea.