An electrical signal travels close to the speed of light (not the electrons). Even when of course no light travels inside the copper.

If something oscillates at 1 GHz, 15 cm down the wire the phase is opposite. To me it's perfectly correct to say that speed of light affects the design a lot and in many places probably is a bottleneck.

Your car does not travel even close to the speed of light for it to matter.

But electrical signals do.

More charitably, charge carriers do move much more slowly than the electric field they transmit[0], and while you’re correct that the time-varying electric field in a processor is not light (nor even a radio wave), if the chips were much larger or much higher frequency the chips and buses would risk becoming antennas and having all the problems that would bring — 5 Ghz ~= 6cm wavelength [1] ~= 3cm half-wave dipole.

[0] https://en.m.wikipedia.org/wiki/Speed_of_electricity

[1] http://www.wolframalpha.com/input/?i=c%2F5ghz

Edit: if the chips were much larger. Smaller chips can go faster without becoming antennae.