Do speaker wires have to be the same length for each speaker?

Sure..., and all of the wires inside of every piece of equipment must be the same length for both channels.

And, all "mirror image" parts in both channels must sit equidistant from the power supply.

The universe is at rest when they are but no.  

They must be the same length, or you will hear an echo.

Have different length cables and there’s no echo or any other issues

Nice if viable but not always possible.