I'd wonder is some cities wouldn't avoid this like the plague... they'd have to set aside a lot of land and give up all development/tax opportunities on it for 10 years. I suppose the Feds would absorb the expense of actually building everything, but it seems it would be a hassle for some of the smaller cities...
You're right. Smaller cities wouldn't, for the most part, want to mess with competing for the honor of being the US Capital. Anymore than small cities would try for the Olympics OTL.