I'm not sure I can explain any more clearly. If someone's not interested in math and they have to make a gameplay decision based on getting +/-1 it's easier for them to work out how much that matters than making a gameplay decision based on whether or not they have advantage.
As to the design...
It's sort of hard to say, really; the difficulty with "fighters" is that a high-level fighter does very much the same kinds of things as a low-level fighter. I bring up Three Kingdoms and the Illiad because the narrative presents folks like Achilles and Guan Yu as epic heroes that are the...
Some of them fit straight in easily. Pathfinder Gunslinger/Swashbuckler would be a Rogue version of the Battle Master archetype (panache/grit points and maneuvers), Inquisitor would be a teamwork-centered Paladin archetype, Summoner would be something like Beastmaster Ranger ported over into...
Half the cast of Three Kingdoms, certainly. The Illiad, but there's some divine intervention going on in that story. Roland (song thereof), Rodrigo Diaz ("El Cid"). Any of the Knights of the Round Table. Cast of the Heike. Heroes out of Norse sagas, my knowledge in this area isn't extensive but...
Advantage/disadvantage is my least favorite thing about 5e; it's too binary (so multiple sources of advantage/disadvantage just don't do anything), it makes the math frustrating if you have people at the table who aren't that interested in it, and then there are characters who can always have...
I'm looking at the anydice results for this and I really like it; your average starting scores shouldn't be much higher (the mean is still 13 and you've got around a 70% chance of sitting between 11 and 15 compared to around a 60% chance on 4d6 drop lowest) but you don't see as many extreme...
Not sure you'd end up with characters who were good at all saves. There's still the proficiency bonus, and characters still won't have good stats for all three saves.
From a game-balance standpoint guns seem less odd when compared to 5e Cantrips. Pathfinder represents guns as high-damage ranged weapons working off of touch AC, which isn't that far off of just knowing Eldritch Blast or Ray of Frost.
I might suggest considering the mechanical effects of racial stat mods. Most classes in 5e get attack bonus/damage bonus off of one stat, so it feels like you're handicapping yourself by playing a race that doesn't get a bonus to the stat that your class runs off of, and you end up with a more...
It might be interesting to do the 3e Fort/Ref/Will saves but let you apply the higher of two specific stat mods to the saves (Fort = Str or Con, Ref = Dex or Int, Will = Wis or Cha). It'd let you apply any attribute to a save as in 5e, and reduce the multiple-attribute-dependency of some classes...