A-HA! IT HAPPENED AGAIN.
I hooked up (literally) my Wii at my apartment after week of inactivity.
I have 3 wireless connections save on my Wii, for my apartment, my parent's house, and my friend's place. I switched the connection back to my own router. I did not test the connection.
Sure enough, it hanged after starting up the Mii Channel, which didn't start at all, just froze at a black screen for several minutes while my Remote was also excommunicated (all lights flashing upon input).
So I powered it off, and restarted the Wii. Went back to the Mii Channel, sat thru another black screen for about 30sec, AND SURE ENOUGH, I WAS RECEIVING NEW MII'S THAT WERE SENT TO ME.
So here's what I think is going on. I never gave the Wii any idle time, so it had no chance to make a background connection and perform downloads. So before loading a channel, the Wii tries to perform a complete connection test and login, and then receive the incoming Miis. It had to make a brand new connection test because it had to switch over to a different wireless setting. It may not hang before loading a disc-based-game because the disc channel does not involve an internet connection, so the Wii will just resume connection/login/downloads after the gaming session during standard idle time. But it may hang before loading any channel that involves data exchange with the interweb. If somehow the Wii doesn't easily restore its wireless connection after inactivity, it may attempt to make a complete reconnect.
Why it chooses to perform the reconnect right before a channel, I do not know. It's stupid like that.
Just because.