The majority of large multichannel amps (up to 200W per channel) rely on a single 15A or 20A power supply. Some quick examples of big multichannel amps with a single 15A or 20A power supply include Outlaw's 7700 and 7200 (both 200Wx7), Lexicon's LX-7 (200Wx7), Emotiva's MPS-1 (200Wx7), and Parasound's Halo A51 (250Wx5) - there are others, certainly, but those came to mind. As you say, the basic physics (15A or even 20A circuits at 120V) says that you will run out of amperage before you max out all of the amp channels. Of course, the source material and speakers that would push seven or even five channels to those levels is pretty frightening to consider (and improbable, for that matter), which I think is why there's not a lot of fuss usually made about the reality behind the numbers.

Outlaw had an amp in the works that we may still see at some point - it was a 300Wx7 amp that they ended up going back to the drawing board with because of heat dissipation issues. It was going to have two separate power supplies (both of which I believe were capable of connecting to 20A circuits). Likewise, Anthem's Statement P5 (325Wx5) has two power supplies that Anthem recommends connecting to separate circuits.