So, I had some quick thoughts on factions in Fallout 4 while taking a shower today and wanted to share them... This is only just about the main four, obviously.
Firstly, I honestly feel that the Institute and the Railroad were meant to be the main two factions. They are the ones which seems to be truly against one another from de' start (as nemesis). Like, these were the two that Bethesda worked on and probably based the MQ around first. They are also the ones that the MQ likes to introduce you to (BoS can easily be ignored).
As for the other main ones... I feel that the Minuteman were originally meant to be at The Castle. I had a feeling that their questline probably would've started at The Castle with you having to go into the armory to get the suit of Power Armor and help defend The Castle from a huge attack of Gunners that has been slowly destroying the Minuteman... It makes more sense for Preston and rest of them to retreat there and for the Mirelurks to never have been there in the first place. (Hell, even take it a step further and allow the player to side with the Gunners. Like the Gunners could already broken down the walls, like the Mirelurks did, and are trying to get inside and you help the Gunners get inside then given the choice to pick a side. You know, defend the Gunners and lock up the doors again and then go to the Power Armor to defeat the rest of them or help the Gunners)...
BUT I feel this idea was scrapped mostly to give the player a 4th faction that can't be failed. Which is why you meet them so early on, even though it makes no sense, and get everything much easier. It was made to be a faction that you can never be enemies with and a faction that can be allied with any other faction, so that you can complete the MQ no matter what. Which means they have to be the first faction you meet and to always be there for ya. At least we know that they are optional to meet but if you follow the MQ normally, you do meet them. (Them being optional what really got me thinking on this).
And as for the Brotherhood... I feel that the Brotherhood was added just for nostalgia AND to be an easier route, so to say. Think about this, the Institute and Railroad symbolizes two knights that are going at it, blocking/parrying one another's moves perfectly... The Brotherhood is that third stronger knight that just decided to be a dike and run in while the two were busy and take them both down... I feel this way mostly because the Brotherhood Paladins are actually the toughest NPCs in the game, as proven by in FFA battles that people has done... The Brotherhood ALWAYS WINS and because of Liberty Prime. Seriously, once the Brotherhood has him active... Their enemies are completely [censored]. At least the other factions have to think up on plans to take each other out. Brotherhood just kinda stomps all other factions with their superior skills and technology...
Anyways, this is just my thoughts on the general reasons why the factions are as they are in-game right now. Now, my thoughts on their morality and such? That's for another thread and requires a lot more of thinking... At least for three of the four factions. Minuteman are honestly pretty easy to explain who they are and what they wanna do (and their flaws).