In part, some of your "design flaws" are the fault of the player base and as odd as this may sound to some people, BGS's willingness to listen to the players.
A lot of what you see in Fallout 4, was being discussed in these forums as far back as Fallout 3's release.
One of the things that the majority of the people wanted was to continue to play after the main quest was completed. Fallout 3 ended at the main quest and in order for BGS to "give the people what they wanted" they had to retcon their own ending. People wanted to play on and on after the game ended and continue to develop their character. There is no way BGS or any other game studio can create an map large enough filled with enough unique quests that would allow someone to play the game indefinitely and pack it all on anyone's hard drive much less be able to do it in the three or four years of development time allotted. If you don't like doing the same set of quests and clearing the same area and looting the same chest over and over again, you should have been here on these forums lending your voice to the "No the game should end when the main quest does" minority.
People have complained that BGS has taken Fallout 4 in a new direction and it isn't the same as it was. This is true, but your complaint that there is no opportunity for a diplomatic resolution is a complaint that BGS has taken Interplay's lead. There has never been a diplomatic resolution between the major factions in any Fallout game. The closest that there has been to a diplomatic resolution was in one of the endings in Fallout: NV but that was no resolution but a rather fragile truce, since everyone is still staring through gun sights at everyone else. At least one faction always is defeated in the Fallout universe and usually destroyed. This should not be a surprise to you, or did you actually believe the catch phrase for the entire Fallout series, "Diplomacy. Diplomacy never changes."
Yes the factions are comprised of sentient creatures. You pretty much cannot have a faction made up of beings that have no awareness of themselves and their surroundings. That does not mean they must be peaceful or even reasonable.
The Minutemen are by far the most reasonable faction in the Commonwealth. All you have to do to keep them from going on a killing spree is to not attack them or those they protect. They function as a para-military police force that is normally in a defensive posture (that's normally, not always) but will become very aggressive if you threaten them, or the people they protect. You leave them and theirs alone, they will probably leave you alone. Initially they are non-hostile to all other major factions. Initially, their only enemies are raiders and super mutants (as strange as it may seem, these are perceived as threats to themselves and those they protect).
The BoS are basically both technophiles and technophobes. There is bad technology, there is good technology and there is good technology that is too powerful for the average wastelander. On the West Coast the BoS will take the too powerful technology away from you and will kill you if you resist. On the East Coast the BoS won't do anything about your possession of too powerful technology (they won't like it, but they won't do anything about it) unless you start shooting at them. FEV and synths (among other things) are classified as bad technology and they will kill you for using it or harboring it.
Right or wrong, the Railroad believes that the Gen3 synths are self aware and self actualizing. There is an ongoing debate among them as to whether the Gen1 and Gen2 synths should be included in this category. Their one and only goal is to rescue synths from bondage and get them some place where the synth can live a "normal" life.
The Institute are pure technophiles. They never ask themselves if they should do something, their only concern is if they can do something. Anyone that is not a member of the Institute is a potential test subject. While initially not overtly aggressive, they are very aggressive covertly. They DO replace people with their synth infiltration units. Whether they have in the past or not, they do currently seek to keep the Commonwealth in an unstable state as a self defense measure. They have kidnapped people of the Commonwealth and experimented on them. They have used the FEV on some of their test subjects. Considering the number of super mutants infesting the Commonwealth, this has probably happened to more than a just handful of wastelanders. Right or wrong, the Institute regards synths simply as machines. Synths are property, nothing more than a sophisticated electric toothbrush. The escapes of synths are viewed as programming errors and nothing more. Once the bugs in the programming are corrected, there will be no more synths believing in self determination.
The average wastelander in the Commonwealth views the Institute as the boogieman. A shadowy organization that comes in the night and takes people away, never to be seen again. They have been known to replace people with their synth infiltration units. There is a debate going on in other threads as to whether the Institute actually tried to help set up the Commonwealth Provisional Government or sent infiltration units in to kill the delegates. What really happened is in doubt, but what really happened ultimately doesn't matter. The average wastelander believes the Institute killed all the delegates and the Institute has done nothing to disabuse them of this idea, As a matter of fact, everything the Institute does only reinforces this idea. Most wastelanders agree with the BoS and view synths as an abomination and will destroy any they find.
There is no diplomatic approach that can reconcile these differences. The Railroad believes synths are essentially, people. The Institute regards them as toasters. Even if you could convince the Institute that synths are people (which you can't), they still need them as a workforce and won't let them go. As Director the SS could in theory end synth production, but the Institute is still going to need a workforce.
The BoS (and the wastelanders in general) believe that synths are bad technology and need to be destroyed. Even if the synths didn't exist, the BoS would be frothing at the mouth over the experiments with FEV. If you don't understand that last bit, you really need to read up on the origin of the Brotherhood of Steel. The BoS WILL destroy the Institute and if they can, the knowledge pertaining to synth production and FEV, or be destroyed trying.
While it is conceivable that the Railroad and the BoS could work together to destroy a common enemy (the Institute), that alliance would only last until the Institute was destroyed. You could never be able to convince the Railroad to allow the Brotherhood to hunt down all synths and destroy them, and you could never be able to convince the Brotherhood that synths must be helped. With the Institute out of the picture, there is no common ground.
The Minutemen are a wildcard. Early in the game they can pretty much go in any direction you wish to take them. As an organization, they have no strong opinions about the other major factions since initially they do not perceive the other three major factions a threat to the stability they are trying to gain. Their only real concern is that they want the raiders and super mutants to stop killing settlers and caravans. Because of their history, individuals in the Minutemen could easily have a grudge against the Gunners, you could consider a major minor faction. The Minutemen's ranks are drawn from the general population, who dislike the Institute and Railroad. They are apprehensive of the Brotherhood when they show up. Late in the game, they will have a real problem with the Institute when their settlements start getting attacked by synths. The Minutemen can have mistrustful but peaceful relationships with the Railroad and/or the Brotherhood of Steel, but the attacks by the Institute synths preclude and sort of peace with them. Again, as Director the SS could halt the synth attacks on settlements, but by then the damage has already been done. Any peace between the two will have to wait at least another generation.
This is basically the way the story was written. This is the way it has always been written. Somebody always gets wasted in Fallout. It is true that there isn't much diplomacy in Fallout 4, but even in the games that had a lot of it, if you wanted to complete the main quest, you eventually had to pick a side and do some killing.