As I continue to consider why this bothers me so much (it shouldn't, I don't even care about Smash Brothers), I think I've reached a way to articulate my frustration.
Nintendo's problems with online go much deeper than simply still using friend codes. That is just a symptom; the disease is that Nintendo has, for a long time, either not taken networking seriously or has viewed networking as something which is actively hostile to their business interests.
That is the real core problem. Getting rid of friend codes entirely and finally creating a standard account system does not fix this problem. What constitutes "good" networking is a rapidly and constantly moving target -- just 7 years ago iOS didn't exist, Android didn't exist, Facebook didn't exist. Youtube had just been created. Online communities and general networking is advancing extremely rapidly, and so when Nintendo finally and reluctantly accepts a standard account system, they will already be even farther behind because the competition is smart and dedicated and constantly moving forward.
The solution, then, is not any individual step or fix, but a totally new perspective; Nintendo has to embrace networking, and not just view it as a check box that needs to be ticked. It has to view the internet -- with all its Zelda porn and illegal streams and 8 bit emulators -- as a friend and ally.
Because if they don't, they will keep falling further and further behind those who do.