What is a faction and what is the point of them? Well, in a multiplayer setting, sectionalized player groups serve two main functions. The first is to serve as a source of conflict. Pitting players against eachother works to serve as endless, unique, repeatable content. The second is to serve as separate experiences, with different choices, environments, and actions.
STO is kind of weak on both accounts. PVP is in shambles, and things like Featured Episodes and New Romulus are more or less the same thing for both sides with only slightly varying dialog options. Things like Lockbox ships and Reputation tracts only compound the issue.
Not to say that STO doesn't have it's strengths in those areas. The wide variety of ships and abilities allows for thousands of playstyles (Even if a fair number of them are broken) and makes every player different, and the non-featured episode content is very unique to the point that outside of the Foundry, you actually cannot fight the Fek'lhir as a Fed.
I find this interesting because you can make so many decisions about your Captain, Crew, and Ship, but there's not a whole lot of choice about the situations you can find yourself in. This problem goes beyond Factions, and possibly lies within the actual design of the game itself.
The structure of STO is very rigid, funneling the player from one end of the map to the other, with only a handful actions to take between point A and point B. The perfect example of this is "The Cure: Ground". It's and endless slog from one end of the mission to the other, doing repetitive actions as you ping-pong your way across the map, and surprise, surprise, the mission is the same no matter what side you play as.
The only ways to fix this is to make almost everything unique based upon what you are and what you do, or, to make everything so organic it's different every time. I think the latter option has more strength to it as screwing around in a sandbox offers way more possibilities than "Go here, do this". I think the game would be a lot stronger if the game were set up this way, not only justifying the existence of factions, but also allowing a lot more options to what we do, and how we interact with eachother, and the game.
I think that a lot of story missions would benefit from being things we "find" while gallivanting throughout the galaxy rather than things handed to us via a dialog box. I've spoken before how I think that there should be full on Featured Episode series hidden in exploration clusters, and I still stand by it.
But the more I think about it, I wonder if the whole game should be treated that way. Where instead of being told to visit Droanza Station, you have to visit it and ask about the strange blue lights, but only after you find a strange Cardassian Ship floating in the depths of space.....
TL;DR: In essence, the strengths that STO possesses make the weaknesses stand out even more. The biggest weakness being the ridgedness of STO's progression and story. If STO was more like a sandbox, and there were more options of where you could go, and what you could do when you got there; the other problems like factions and content, would basically solve themselves.
I agree that STO could do with a more 'organic' system of content delivery; I do like the sound of your proposal (in fact, unless I've completely misunderstood you, some of my recent suggestions for exploration are not so far removed from this), but could you be a little more specific about how you feel this will strengthen the factions? I'm not sure I fully grasp your intent there.