Most of your tactical analysis is bad and your argument is still riddled with errors. E.g. the claim that "such a PC [Mobile Sharpshooter] is so focused on defense and survival that he is subpar in combat to most other builds" is laughable. Nope. He hardly gave up anything to get his versatile defensive capabilities: one feat (Mobile), one free spell pick (Expeditious Retreat), one regular spell pick (Shield, which is ubiquitous among EKs), and three skills (Athletics, Stealth, Perception) which have both offensive and defensive uses--and you claim that a Valor Bard is going to do comparable damage? (News flash: Valor Bards at 5th level don't even have Extra Attack, nor a fighting style, nor Sharpshooter. Against a high-AC foe like the AC 17 githyanki, you're doing only 42% of the fighter's damage even if you have Str 16 and a greatsword. Against a low-AC foe like an AC 13 Hill Giant, you're doing even less, 37%. Not remotely comparable.)
Playing defense as an integrated party typically works a little bit differently than playing defense solo: it involves things like crowd control, Wall of Force on the biggest bad guy, Web spells to give enemies disadvantage and make kiting easier, and tanky PCs grappling/proning enemies. The implementation changes but the point does not: you still tend to wind up doing better with versatility (good offense and excellent defense) than you do going all-in on offense.
Not that defense is a trump card. Again, sometimes, despite defense being generally cheaper and more efficient than offense, some other tactic like healing or sneaking is even more efficient.
Yeah, you can make the claims that my analysis is bad, but they doesn't make it true. As for errors, I do that all of the time. I'm old and make mistakes. Deal with it. It doesn't mean your opinion is correct, it just means that I'm old and make mistakes.
As an example, your entire Githyanki example is kind of laughable. Seriously. You picked foes who did not have ranged attacks, just so that your mobile build get easily get away. What a terrible one sided example. A Young Dragon could easily defeat your EK solo build at a much lower CR as long as the encounter does not start at hundreds of feet apart. Ditto for a Frost Giant, even with disadvantage later in the encounter at range.
And yes, your EK build is gimped a little bit as a fighter. You did not declare that he would be taking the Archery fighting style (and your PC's DPR drops by 3.5 points if he doesn't take that style), but that is a fairly typical assumption with such a PC. So assuming a 16 Dex, here is how your PC compares DPR to other normal fighter builds against AC 16 at level 5:
EK Sharp: 14.45 (i.e. -5/+10 which does the best DPR)
EK Melee: 8.7 (rapier)
18 Str Duel: 13.25 +2 AC
18 Str GWF: 15.63
16 Str GWM: 13.97 (normal, not including extra attack due to killing a foe which is impossible to figure out, but if it were 1 attack in 6, DPR would climb another 1.1 points)
16 Str GWM: 14.3 (-5/+10, not including extra attack due to killing a foe which is impossible to figure out, but if it were 1 attack in 6, DPR would climb another 1.1 points)
16 Dex Ranger Sharp: 19.63
So compared to the Ranger Sharpshooter, the EK Sharpshoot is giving up over 5 DPR. Your PC is not a striker, he's a defender that doesn't typically defend.
So you are correct. On the surface, your PC does about the same damage as other fighter PCs assuming that your PC is not in melee. The other fighter builds tend to have 1 (or 3) better AC (heavy armor instead of medium) than the EK build and any of these PCs could be an EK with all of the other advantages that gives (like a Shield spell 3 times a day or Expeditious Retreat). Granted, these PCs are somewhat lousy at ranged attacks, but them having to do ranged attacks would seem to be a lot less frequent than your PC having to do melee attacks (shy of your PC totally kiting from the next room over or some such most of the time).
The issue is that you only (for the most part) do damage and kit. You do not soak up melee attacks like other Fighters, so those attacks (and other shorter range ranged attacks/spells) get spread out over the rest of the party. If you do decide to attack in melee and soak up attacks, your damage goes down the toilet compared to other fighters (alternatively, you could use the Help action to give them advantage, but even that is probably subpar). And if you are kiting far back to the point that monsters rarely attack you due to range, then if you do get attacked, other PCs cannot reach you in time to help. Your PC can sometimes help other PCs (e.g. pour a potion down their throat, etc.) due to your mobility, but not maybe so often the other way around.
Finally, I prefer a Battle Master to a EK since I think that they are much more effective, especially at lower to mid levels. But, that is subjective.
So yeah, I claim that this is a meh PC. Not good. Not bad. Just not a team oriented PC. A fighter who does similar damage, but does not himself often take damage. Kind of like a selfish PC. I understand this type of design built in preferable behavior for a Mage or Bard, but not a Fighter. JMO.
And yeah, I suspect that less than 1% of all players play solo games. It might be slightly higher than this, but who cares? The game is made to be played by a group of players, not just one player and the DM. So analysis leaning towards solo PCs tends to be less than useful for the vast majority of D&D players.
But offensive specialization, especially DPR specialization, past a certain point is really expensive in 5E and not usually worth it.
I agree with this. I just don't agree that such specialization stops at level 5. For me, it is closer to level 12 or even higher.
