Tutara
Adventurer
I don't think it's arbitrary. There are definitely classes which tend towards ranged attacks and Fighter isn't really focused on that mechanically. Their armor indicates they will be near enough to creatures to be targeted in melee. The small number of archery feats and the increase in the number of feats a fighter gets tends to tilt toward melee where there are many more feats to be found. Their subclasses, when they make a choice between melee and ranged, tend to make more choices towards melee.
You can absolutely make a great ranged-focus fighter. But I think it's fair to say the fighter as mechanically written along with the rest of the rules tends more towards melee than ranged focus. And that halflings have some somewhat arbitrary limits on their melee focused abilities as well. You can certainly make a melee halfling fighter, but I think it's correct to characterize the rules as somewhat discouraging that.
Then if you compare it to the data we got, halfling ranks last for Fighter choices, and is completely off the list for Paladin.
I'm not sure which written abilities of the fighter lend themselves to melee but not to ranged combat. As far as I can tell, they all work fine at range as well. The presence of the Archery Fighting Style, for example, seems to indicate that a ranged fighter is within the expected parameters. You could argue feats like Great Weapon Master or Polearm Master, but then there are feats like Crossbow Expert and Sharpshooter to counterbalance.
I'm not disagreeing - you can indeed make a great ranged-focus fighter. I'm just not sure what the rogue or ranger offers that makes them better at engaging at range.