Again I'm wondering have you read the corebooks or actually played 5e? Serious question, what is the extent of your experience with 5e?
So, a Melee Battlemaster has 16 powers, a Ranged Battlemaster has 12.
Uhm no... first they are maneuvers not powers and second all Battle Masters get a total of 9 by 15th level... so no BattleMaster has 16 or 12 maneuvers...
A champion's Improved Critical works with all weapons, but, considering that melee weapons out damage dice ranged weapons, we're back to melee weapons being more effective. Never minding that you need to start spending feats in order to make ranged attacking effective - removing things like disadvantage and cover penalties, none of which actually apply to melee attacks. Oh, and let's not forget that because you have a bow in hand, you no longer get Opportunity Attacks and cannot benefit from a shield.
Melee weapons being more effective how? Pure damage dealing? Only if you go two-handed, which means...
1. You can't be a small race or you suffer disadvantage on attacks
2. You aren't wearing a shield
3. You can only ever use ranged combat effectively within 30ft (Str based) without suffering disadvantage to attacks.
4. You must engage foes in melee to attack thus you are being attacked in return and are open to AoO
5. Can't use stealth while fighting
As to your other points... they don't make any sense.
You don't
have to spend feats to be effective in ranged combat, though you should if that's what you want to focus on. the range on a longbow (without disadvantage on attacks) is 150ft... Most melee combatants can't even reach you before you've gotten multiple attacks off... You can also move and hide as a ranged combatant after attacking (since we're assuming cover is common enough to pose penalties in enough fights that a feat is
needed to compensate

). Of course I'm not understanding how exactly they would get to the archer if they stay under cover? He'd just continue to shoot at them with the penalties until the law of averages allowed him to kill them... same with an opponent engaged with your ally, it's a free attack where you're not suffering an attack in return or an AoO. I think in your effort to vastly simplify "effective" you've totally glossed over the actual advantages of ranged combat...
But, yeah, just as effective as a melee fighter. Less powers, less damage, lower AC, same movement rates, and you are forced to burn feats. Totally just as effective.
The same amount of powers...ability to snipe, stealth and surprise from up to 150ft away, higher average initiative, no feats are necessary, suffers less direct attacks and AoO (so no need for an AC that is as high as a meatshield)... so yeah I'd say just as effective if not more since they can also melee with finesse weapons while using a shield if necessary. Of course if you had read the fighter section or even the character boards on the WotC forums you'd already know most of this. In fact if it wasn't for the damage disparity there would literally be no reason to ever play a strength fighter...
Yup, in 4e, fighters were, by and large, restricted to basic attacks with a bow. Pretty much the same as a 5e fighter.
Except for the 9 maneuvers a Battle Master can use with a ranged weapon... or the improved crits a champion gets with it... or the spells an EK can use to enhance his ranged attacks... so yeah just like 4e.
Hey, you want to make a 5e bow fighter? Go right ahead. I'll be over here giggling at you as you do about half as much damage and get hit far more often. Let's not forget that while you take things like Sharpshooter feats, I take things like Heavy Armor (DR 3 more or less) or Sentinel (free attacks and turns me into a pretty much straight up 4e style fighter.)
How does an archer fighter get hit more attacking from 150ft away against targets that are continuously keeping cover? Now you're really just showing your ignorance of the system. Also just an FYI... sharpshooter is a single feat that not only negates all those penalties for cover, increases my effective range to 600ft but also allows me to take a -5 to hit in order to increase my damage by 10 (and don't forget I already get a +2 with ranged weapons from archery style)... but yeah you keep laughing from 600ft away...
Although, all that aside, I cannot for the life of me find the rules that let fighters add their Dex to damage with ranged weapons. I know it's there, but, where the heck is it?
It's under damage rolls in the combat section of the PHB...
