Does a radio station main amplifier work at the speed of light?
you can't accelerate the electrons that quickly.


I think the problem lies in a misconception.  The electrons don't move at the speed of light, in fact if you could 'tag' an individual electron coming into a wire and then sense when it leaves you could measure it with a stop watch in a reasonable length of cable.

The effect of the electron, or in other words the wave that is generated when an electron is pushed into a conductor, can be sensed almost at the speed of light on the other end of the conductor, but the individual electron you pushed onto the cable will not appear there for some time based on current, voltage, etc.

So the amplifier does not accelerate electrons to anywhere near the speed of light.  It induces waves in the electrons in the cables, or amplifier, which are sensed by the semiconductors which induce waves in other cables and other semiconductors.

There is some inherent delay with every amplifier, but it's so small as to be unnoticeable by human ears.

Note that if amplifier introduced significant delay, then BBC broadcasts on NPR stations in the US would be delayed much more than the few hundred mS it already is.