Increased resistance in the house wiring, due to smaller gauge or greater length, will produce a voltage loss just as readily as in the power cord. And in fact most likely to an even greater degree (since the combined current draws of multiple devices are likely to be flowing through it, rather than the current draw of just one device, and voltage drop equals current times resistance).
Probably why many advocate dedicated circuits. I would start with dedicated circuits, as short a run as possible from the panel, then an adequate gauge power cord (the same gauge or larger than the romex) that is as short as practical.