But that's exactly what Star Trek Infinite Space from Gameforge provides -- and for free, too.
Players can create a captain in the Federation or Klingon Empire circa season 3 of Deep Space Nine. They then begin their career of conquering the stars through three types of mission: those that advance the game's plot; self-contained "battle scenarios" that offer a compact, action-oriented mission; and "free exploration" mode, which offers the authentic Star Trek "seek out new life and new civilizations" experience.
Progression through the game gives players access to better ships, eventually allowing them to pilot iconic classes of vessel such as Galaxy (Enterprise-D) and Intrepid (Voyager) class ships. Alongside that, players can upgrade their skills along with those of their crew members, which come into play both in combat and when sending an Away Team on a remote mission.
Infinite Space diverges from the model set by Cryptic's Star Trek Online in several key ways. Firstly, the space exploration and combat is done from a top-down view, albeit with some impressive 3D graphics and a fully controllable camera. Secondly, Away Team missions aren't led by the player's character -- instead, in a more authentic nod to Starfleet protocol, you as the captain must remain behind on your ship while the crew you sent on the mission report back to you over the communications system. They frequently run into trouble and call you to make a decision for them -- sometimes these involve making RPG-style skill checks, other times they're moral choices that can cause the mission to unfold in different ways.
Outside of missions, players can hang out in numerous bars scattered around the Star Trek universe. These act as the main social hubs of the game, and are the only part which are truly massively multiplayer -- the remainder of the game is instanced for you and your group if you have one. A nice touch is that the loading screen for a mission shows your ships (and those of any party members) travelling at warp speed to your destination.