There are actually very many systems and listeners that can identify the difference power cords make. It seems counterintiutive that a couple of meters of cable can make a difference, but many listeners find the difference audible. There are plenty of other threads as to the empirical reasons for this.
However, in order of priority and value for money, it makes sense to ensure that the wiring and sockets that precede the mains cord are up to scratch. The case of the dimming lights that prompted this particular thread exemplifies this perfectly.