802.11 networks, the kind of wireless technology that DS systems and Wiis use to connect to the web and each other, can handle about 50-100 devices being in the same area before things really grind to a halt. 802.11 devices use a narrow portion of 2.4 Ghz range to transmit and whenever a device "hears" another 802.11 packet of data from another device, it refrains from transmitting until that packet has passed. While a few devices won't have any issues under this system, once you start hitting any more than that, you will see some serious slow down and lag. Additionally, any strong radio waves in the immediate area or any large number of additional electronic devices in the immediate vicinity can increase that interference significantly.
The Wii also uses another wireless technology, Bluetooth, to connect to the wiimotes. Fortunately, wiimotes and the system communicate under passkeys that lock the Wii and the controller to one another. That's why you can see a series of stations at Nintendo events, all using wireless controllers, that function just fine close to other stations. Bluetooth devices also use a pseudo-random switching system, to make small changes to the frequency about 1600 times per second. This further prevents interference with the devices.
However, according to bluetooth experts, the chances of two bluetooth devices in close range creating interference for each other is 1/79. Considering that 1600 changes are made per second, you can see the bluetooth devices are robust enough to handle regular spurts of interference here and there. However, the more devices you pack into one space, the more often that 1-in-79 chance interference actually happens. Bluetooth devices are also more robust than 802.11 technology when it comes to outside interference from televisions, power cables, cell phones and other electronic devices because they use the entire 2.4Ghz range to communicate and change rapidly. Unfortunately, they are not 100% resistent, so the more devices you pack into a single space, the more potential interference you encounter.
So imagine for a moment that you are using the Wii and wireless controllers to run a local tournament. It's the beginning of th event, which means lots of 4-man warm-ups and teams matches following. That means at each station, you have 5 bluetooth enabled devices (Wii + 4 controllers). Assuming you have 10 stations set up, that's 50 bluetooth enabled devices, plus the televisions, power strips, cell phones, DS systems and computers. Bluetooth has a maximum range of about 30 feet and an optimal range of 15 feet, so the closer any of these devices come to one another, the more likely interference will occur. Additionally, if any of the devices are networked together, for instance, some players are using the DS to play Pokemon between rounds, the interference increases. That interference will hurt the game of Pokemon more than it will hurt the game of Smash, but it will effect the Wiimotes. I am not terribly good at math, so someone else will have to calculate how a 1/79 chance, each of the 1600 changes per second, times 50 devices will play out and how often we can expect interference to occur.
So considering all of this, the question is, what is an acceptable amount of interference? As you can see, even small events are going to experience it in some fashion. It might not be enough to make the tournament unplayable, but its possible that the interference will effect the outcome of the matches if normal device functionality is interupted for a fraction of a second, every few seconds. Imagine attempting to run an event the size of FC, with 30 stations, 150 devices, plus 200 people talking on cell phones, playing on their DS and laptops and running power to TVs across a mile or so of cable. Sure not ALL of the devices will be within the 30 foot range, but they will overlap with dozens of potentially interfering devices no matter how well that gymnasium is arranged.
On top of all that, one has to consider the actual operation of the tourament and what kind of effect resetting the system over and over again to sync controllers will have on the ability to run the tournament smoothly. It will waste about 5 minutes each time the system has to be reset and controllers are synced. And since you will run into more problems if any other systems are resynced within the 30-foot range at the same time, even more time will be wasted staggering the reboot of systems within a certain range. If we allow wireless controllers at Brawl events, tournament organizers can expect to run about 25-30% longer easily than they have with Melee.