Wow... an avalanche. Let me try my best to defend my reasoning.
First of all, I didn't say that Jon isn't AA, just that in my opinion Dany is more likely candidate.
Every hero needs to make sacrifice great enough to prove his worth. In AA case he decided to kill his beloved wife in order to save the world. Yigrrite doesn't compare, if Jon is AA, the greater sacrifice is coming his way, who could it be I cannot begin to guess.
At the moment NW can be compared to the Lightbringer only in the sense that it is failing his AA (Jon) in every aspect as Lightbringer did, before great hero decided to temper it in the blood of innocent woman. Oath they take sounds very poetic, but let's check some facts: At the beginning of the books, sworn brother runs FROM the Others instead fighting them and protecting the realm, Mance Ryder betrays his oaths and becomes King-beyond-the-wall, Sworn brothers rebel and kill old Bear while running away from wraiths, even Jon betrays the oath taking a spear-wife. Sworn brothers, in the very least, try to kill Jon - their Lord Commander. Where is this in the oaths? If NW is to become the Lightbringer, something must be DRASTICALLY changed in the way they fulfill their oaths.
Everything that I read so far in ASoIaF goes to one point - DON'T BE FOOLED BY GREAT WORDS. Words are wind. GRRM is maester of words, and he is using them to conjure better glamours than Mel.
But remember... The NW over the century forgot their true purpose... They thought they were created to keep out the Wildlings... That's not true... They were created to keep out the Others. But over time, Nobel houses stop sending their sons to the wall and started sending murderers and rapers... Jon is bringing an end to that by allowing the Wildlings and women to serve on the wall... Women never served on the wall until Jon... Never...
An AA killing his wife to make a sword? Don't make sense... It's too fantasy and that's not GRRM style... If that story was true, Nissa Nissa is the one who truly made the biggest sacrifice... Not AA...
I believe until AA was truly able to let go of his wife emotionally, he wasn't able to do what was needed... His love for her and her love for him was keeping him from forming what needed to be formed... The NW thus the Oath... "I will take no wife"... By taking that vow, AA figurely not literally thrusted his sword through his wife's heart... In other words, he broke her heart...
Jon have put things in motion to make the NW completely independent like they were of old... He started with the loan from the Iron Bank and ending with the Wildliings which have women to replenish their ranks for generations...