Wireless technology was not as cheap, and readily available, back in the day. Calling it an obsession is definitely not warranted when it was, in fact, a nessecity if they wanted to do multiplayer games - especially on the original Game Boy.In the past, Nintendo had a sick wired obsession. You needed wires for everything, for play multiplayer Game Boy games, to connect your GBA on the GCN. I'm pretty glad Nintendo stuck with wireless stuff nowadays.
Input lag is not the only reason wireless isn't much liked. EVO, for example, has banned the wireless Dualshock 3, and Sixaxis, controllers for various reasons. Major reasons being related to how the controllers pair with the console. And since while unpairing your controller to the console your controller will be remembered for about 2 odd seconds, that has the potential to interfere with on-going matches on other set-ups you've been on.Well, aside for this input lag thing (I'm not so smart in this subject, sorry), I don't see any problems with wireless controllers on the tournament play, specially on the Wii U, where is miles easy to pair/unpair a controller and the Pro Controller features an awesome 80-hour battery pack.
Also, the input lag is the primary reason many competitive players dislike wireless. If you haven't noticed pretty much everyone into competitive Smash are incredibly anal about input delay. And as long as there is some input delay, regardless if it is humanly possible to notice it, they more than likely "will". Oh, the wonders of placebo!
As for my personal reasons for disliking it. I just have a bigger appreciation for plugging in a controller and playing. No need to sync up your controller just so you can play. Besides, in a tournament with many, many entrants, the added time you take by syncing up your controller to the consoles, amount to a lot of time. Which could be a non-issue depending on other factors, but even then, you cannot completely disregard it.