While Jon focusing NW on archery is a good idea now, was it really bad for NW to focus on melee weaponry prior to start of the story? Horde of Wildlings attacking the wall is a new development, so likely 99+% of wildling encounters happened on Rangings and the like, where melee is more useful. In addition, practice shooting at horizontal targets 100' away or so is of marginal benefit when shooting at enemies 700' directly below you.
One important corrective: “hordes of wildlings attacking the Wall” is NOT a new development:
“Wildlings have invaded the realm before.“ Jon had heard the tales from Old Nan and Maester Luwin both, back at Winterfell. "Raymun Redbeard led them south in the time of my grandfather’s grandfather, and before him there was a king named Bael the Bard.”“Aye, and long before them came the Horned Lord and the brother kings Gendel and Gorne, and in ancient days Joramun, who blew the Horn of Winter and woke giants from the earth. Each man of them broke his strength on the Wall, or was broken by the power of Winterfell on the far side…”
The Watch is primarily a defensive military force manning a fixed fortification. GRRM’s problems with math aside, it makes a lot more sense to train them in archery and siege weaponry than it does to emphasize hand-to-hand training, given that melee weapons’ arms-length range doesn’t do you much good when you’re on the top of a bloody great wall and the enemy is at the bottom.
Now, ranging is a different story, but I would maintain that Ser Alliser’s godawful training scheme is still a bad one: emphasizing fighting on foot one-on-one is a very bad idea when the Night’s Watch is badly outnumbered by wildling raiders, who are absolutely going to use their advantage of numbers to overwhelm whatever negligable training in the blade a crow gets in boot camp.
To the extent that you’d emphasize melee combat at all in the Watch, it should absolutely be focusing on cavalry tactics, which would allow the Night’s Watch to punch above their weight vis-a-vis the mostly on-foot Wildlings. And cavalry tactics emphasize horsemanship over swordsmanship, because you don’t need to be very good with a sword when you’re thundering down on someone at top horsepower.