Um, this is something of a nit-pick, but you would get 3 attacks (not one). This isn't 3e. You don't need to take a full-round action to get a full suit of attacks. You are right though, in a white room scenario where nothing dissuades anyone from kiting, kiting would become a thing. In the encounters I have actually played, however, I have never seen kiting happen. There was always some factor that stopped such events.
You misunderstand. Javelins are rate-limited by your object interactions. You can no more draw three javelins in a single turn than you can draw three swords. The rules for ammunition prevent this hampering ranged weapons ("Drawing the ammunition from a quiver, case, or other container is part of the attack") but javelins are thrown weapons, not ammunition.
You could throw one javelin and then make two shield bashes on an adjacent target, but you cannot throw three javelins unless you're starting with one javelin in each hand and then draw the third as your object interaction.
I've seen kiting happen rather a lot, especially at low levels. It takes a fairly contrived scenario (e.g. movement only via teleportation gates) to make kiting impossible.
Um, no, my assumption of Dex 19 doesn't. If you use the starting stats or point buy, and you spend two of your stat increases on feats, the highest Dex you can have by level 11 is 19. So, assuming a Dex of 19 isn't an unrealistic penalty at all!
Point buy is a variant rule, but let's say it is point buy or standard array. Dex 15, human, means you start with Dex 16 and Crossbow Expert. By level 11 you've had three more ASIs, which gets you Sharpshooter and Dex 20. QED.
(Using the standard 4d6 roll, the majority of PCs will have at least one ability score of 16+. Point buy is weak, perhaps deliberately on WotC's part.)
Nitpick, but Eldritch Knights can't be disarmed by Battlemaster Disarm due to Weapon Bond.
To address your larger point: yes, the advantage of ranged weapons lies chiefly in their tactical characteristics, not the raw numbers. If all fights were duels between PCs, then yes, if all fights started at 5' range, then melee PCs would have an advantage. (At 10' I don't find your analysis compelling because it neglects initiative--the ranged fighter can get a free round of attacks if he wins initiative, but the reverse is not true for the melee guy, and the ranged guy is more likely to win initiative because he is pumping Dex.) The major advantage of melee fighters at that range would lie in their ability to Grapple/Prone the ranged dude before commencing a beat-down; Dex-based fighters have a tough time escaping from a grapple because they can't use the normal Fighter-y means of escape very effectively (Pushing the enemy away w/ Strength (Athletics)).
But no realistic game takes place entirely under that narrow set of conditions which gives melee the advantage you posit. E.g. most PCs play in parties of at least three PCs, and range-specialized PCs have better mutual support and defensive characteristics in that scenario, no matter whether they're on the salt flats or navigating 2' wide corridors in a stone labyrinth. I gave one example previously, here's another: one ranged dude can Dodge all up in a monster's face while the other two kill the monster. If a melee-heavy party tries that it will just ignore the Dodging guy. Range specialization gives you more tactical options.
Melee does have some advantages, but they're not the numerical ones you have been emphasizing so far. Strength (Athletics) really is the key differentiator for melee PCs; feats like Sentinel and Warcaster can help too. But those advantages are mostly about tanking, not inflicting damage, which means that the optimal party configuration is still (generally) to have the bulk of your firepower be ranged with just enough tanking specialists to provide a front line when needed--and the best tanks aren't warriors anyway.
