Well, that's a much bigger topic than either of us probably realize.
Starfleet is a very important organization for reasons that have nothing to do with its size, which isn't huge. In a lot of ways, trying to keep unity among a dozen disparate civilizations -- some of whom used to actually hate each other -- requires a lot of sensitivity and compromise over who is allowed to do what and when and where.
Starfleet gets the best exploration targets because they were founded to open up the resources of space to the benefit of ALL Federation members and they have earned a lot of credibility on that issue. They are tasked with interstellar security too, for the same reason: they are trusted to be impartial in conflict disputes and exercise tremendous patience not to resolve those conflicts by simply gunning down one side or the other.
The way I'm seeing it is that Starfleet is a smaller piece of a much larger picture and a lot more happens "behind the scenes" than we have ever had a reason to see. As a consequence, there isn't really a sense of "government issue" in their equipment: they have a standardization (for the most part) for what they use and how it's configured, but they still have to obtain that equipment from suppliers or obtain the parts needed to manufacture it themselves. They build their own weapons, they repair their own ships, assemble their own shuttlecraft from scratch. What little they don't make themselves they have made for them at local machine shops at starbases and use the parts to make the final product themselves.
The result is that most starbases and even some starships (flagships in particular) are almost totally self-sufficient for their operational needs. Smaller cruisers and scout ships have to rely on the larger facilities of starbases and civilian colonies and will occasionally have to put in to a port somewhere to use a dry dock, but the flagships have their own industrial fabricators with enough capacity and engineering equipment to practically rebuild themselves if they have enough time and raw materials. Ironically, this means that Starfleet technology is only as advanced as its crews have the capacity to repair: they wouldn't install anything so cutting edge that only a handful of people know anything about it. Quite the opposite: a lot of what goes into a starship is practically "open source" and common enough that anyone in the engineering department will be thoroughly familiar with every part of it by the time he leaves the academy, and even well versed on planned improvements (just in case Starfleet emails them specs for an in-situ retrofit). The rather infamous down side of this is that most visiting aliens on a starship are seeing technology that, to them, might be ten years old or more, and so sabotaging the ship turns out not to be all that difficult...
The ECS: I consider the term "merchant marine" to be a term that was used only because M5 inheritted Daystrom's penchant for anachronisms. The Merchant Marine is
the ECS inasmuch as Starfleet is
UESPA. No doubt Earth is also served by a variety of non-governmental agencies -- corporations, freight lines, tour companies, charities, privateers, etc -- who also operate rather successfully in space: couriers, freighters, ore ships, people movers, grain ships, etc. By the late 22nd century, the Jehovas Witnesses have started wandering the stars, looking for centers of suffering and deprivation and offering relief in exchange for "a few minutes of your time." (Yes, they're kind of annoying, but feeding five thousand people with a loaf of bread and a fish is a lot easier when you have replicator technology). Meanwhile, the Vulcans have their own shipping companies, private merchants and trading families, as do the Andorians, the Bolians, the Tellarites and so on. There are probably a few hundred thousand distinct corporate entities alone that have large footprints in the commercial space industry and a few million people involved in interplanetary and interstellar commerce on one level or another.
As you can sort of see above, I'm trying to get away from some of the "monoculture" portrayals. Even in the 23rd century, even at its presently small size, the Federation is ALOT bigger than Earth, and the Federation members are much more than people who happen to be following Earth's lead. Everyone is contributing in their own way, and their various contributions are what help keep the Federation together. Earth's contribution is this huge exploration fleet that allows them to share resources peacefully without fighting over who gets access to what or fighting pointless wars over "Which one of us is going to have to marry that Elaasian bitch?" etc etc. Other races contribute in other ways we haven't seen because they don't usually involve deep space exploration, each with a specialty (or two) that the Federation could barely function without.