This is an example from a developing country, but it may be illustrative. My dad had a big chunk of money in CDs (some in foreign currency), and his bank went belly up. There is something similar to the FDIC over there, but he was still worried about his money. Well, the end of the story is that all those accounts were absorbed by another bank, and there were absolutely no restrictions on withdrawals, etc.
The thing is, if people have a hard time getting their money from the FDIC (say, in case WAMU goes belly up), then people would panic and start withdrawing their deposits even from financially sound banks. This is something the gov’t won’t allow and can easily fix.