Maybe my components aren't audiophile enough to justify purchasing upgraded power cords.
You won't know until you try it. Do you buy from dealers, or used?
If you have a relationship with a good dealer see if you can borrow a good demo ($1000+) high current capable power cord from them, put it on your amp, plug it directly into the wall and see what difference there is.
If you hear a difference you will have to decide whether that is worth the asking price, and that will answer your question "Do I need upgraded power cables".