Normally I'd just skip commentary when a post gets so long. So I apologize if I screw up any important parts of your manifesto. I'm trimming as much as I can.
Not kensei specific. Versatile weapons are good for any monk, even though they might not always use both hands on the weapon. They may be holding a light, a ranged weapon, or an enemy in their other hand. Two weapon fighting is an option just for a little more ranged damage, short ranged though it is.
You aren't losing the option to draw and throw a spear/trident/handaxe, at any time, or to start combat with the throwable weapons and switch to the martial weapon if you don't need to throw anything, so it's purely a benefit.
I like my waffles with butter.
The longbow is an obviously good choice. The sling allows bludgeoning damage at range. The hand crossbow if you want to be a crossbow expert.
Show of hands: Who took Polearm Master for your monk? Sure, it gives you a reaction attack. . .
Turn to turn, you can choose either higher AC than any other monk or higher damage than any other monk.
The first attack of flurry of blows is immediately after the attack action, so you can't attack, then walk over and flurry. You have to already be in range to flurry. That's going to make at least one of your ranged attacks a little difficult, most of the time.
If you're in a position that you want to make unarmed attacks, then you probably want to just use one of your melee weapons. If you're using a ranged weapon, there's a high chance you don't want to get into melee, and so may appreciate an alternative way to deal more damage as a bonus action.
There is no issue here. Kensei makes archery an option, and if you want to focus on it, you don't have to have great wisdom to still get good AC for an archer. Monks multiclass well with battle master, but that's a benefit, not a problem.
The party might have one or more magic weapons, but they might not have enough for everyone, they might not have every kind of magic weapon, and this is to give the Kensei parity with their unarmed strikes. It's exactly as important as the baseline monk ability. For C, yes, it will be that much better than an unarmed strike. +2 damage is the whole Dueling Fighting Style, or the weapon will have longer reach. And I guess I'll call it D, you will never have enough +1 arrows in the party for everyone who needs them to never have to worry about them. They're only 5% chance on the random tables they show up on, and a party would need several per round of combat.
In the short run, it can be used on top of everything else the monk can already do. It's pretty cost effective if the enemy is tough to hit, or you have some reason to not use flurry.
The most likely weapon you won't have at this level is a +x longbow, since nearly everybody could use one and they hardly show up randomly. If you have a +x whip, a +x longsword, a +x longbow, and a +x sling at level 11, good for you. The rest of us will probably find some times this is useful.
The subclass is fine. By virtue of having the options for the best melee damage, best ranged damage, and best AC among monks, it is the best monk subclass at martial combat.
Speaking of badly thought out game design: In the first case, the character would have no ability to choose different weapons. It would either have the ranged weapon benefit or the melee weapon benefit for most of the game. I can list 5 weapons any kensei would benefit from mastering without going into specific feats or multiclasses: Longsword/Battleaxe, Warhammer, Whip, Longbow, Sling. They don't need that many choices, but they do need more than 1. Balancing the magic weapon bonuses around a cost means that getting a permanent magic weapon isn't totally redundant. It frees up resources for your other abilities to be used more. Giving the same bonus (option) to every weapon is just for convenience. Your suggestion reminds me of the awful scaling on Favored Enemy damage bonuses, where the one you pick at the start of the game could go up to +10 and the one you pick at the end just gets +2. This version is like the kensei, but even more boring and possibly less powerful.
OR
Just have every Kensei end up as a purely unarmed character because Unarmed Strike would always end up as the clear best melee option by level 17, if not earlier, and who cares about themes and identity in a subclass. Kensei can't pick unarmed strike because 1) That's not the point, and 2) That would overshadow almost every melee weapon. At least the whip has reach.