There is nothing saying you need a high STR, Dex or con with a fighter. RAW you can build a fighter with an 8 in all three if you want. If you want to multiclass you need a 13 in either strength or dex.
As for constitution, it isn't a prime ability and in point buy I always dump constitution to 10 on every single fighter I play. The only time I am running a fighter with higher than a 10 constitution is if I am rolling. I always have at least a 14 in ONLY one of strength or dex and more often than not a 16.
Logically with point buy a fighter that is built to be good at combat and good at social skills you should have a 10 constitution, an 16 Str or Dex an an 8 in the one you don't have a 16 in. That is the most complete fighter build you can make and it is the one I routinely make. Sometimes I have 14 in all of I/W/Ch, sometimes I have a 16 in one and 12s in the other two. Like I said that is for a good all around fighter and such a fighter still outrun most Rogues in combat while being good in social situations. If you want to min max instead of being all around then to optimize combat stats then dump the social skills, if you want to optimize social skills then dump the combat stats. It is a pretty simple concept. The same concept is true for a Rogue. If you want a combat focused Rogue you should take a 14 dexterity and a 16 strength and a 14 or 16 constitution and dump the social skills. Such a Rogue will be far more effective in combat than a "traditional" Rogue but will not be as good out of combat.
For some reason people in this board refuse to do these things though and then wonder why their fighters that has a 16 str and 16 con and 8 charisma sucks in social situations. It is because they chose that build!
The skills take care of the social aspects, the story part is either from your background or how you play your character and for the most part the actual class is irrelevant to that unless your theme is a caster.
People talk about "always on" abilities. Fighters right from level 1 can choose many always on fighting styles and they are the only class that can do that at level 1. They also have an always on heavy armor from 1st level, one of two classes that can do this (some subclasses can to). Those things are very significant features.
Bottom line: If you need to be "dominant" in combat you won't be dominant or even good out of combat. If you are ok with being just good in combat then you can be both good in combat and good out of combat.