The vast majority of home circuits are run in a daisy chain from one outlet to the next. Every connection introduces micro-arcing and noise. All the current running to the last component had to go through all those connections. Also every wire is an antenna and brings RFI into the line. So even if your system is the first outlet merely by running to the others introduces more RFI.
The main reason for a dedicated line is to remove all these sources of noise. The difference is big and easy to hear. This noise is present on all AC lines, just much less without all those extra connections. It is not just for the amp, every component benefits. Running more than one line is unnecessary and may even be worse, in that it runs the risk of introducing noise in the form of ground plane differentials.