Either way the audio is a miniscule part of the total current draw of one
of
these players. The battery lifetime difference between full rated power
and
muted is perhaps a few minutes.

What about in full size receivers and amplifiers, from say the 60's
to 80's. I got the impression somewhere that in those devices the
output stage used more than all the prior stages combined, right?

Does accessing memory in an MP3 player etc. take much current?

That's true of pretty much all stereo receivers, but we're not talking about
stereo receivers, we're talking about a portable device capable of
outputting a few milliwatts to a pair of earbuds, not a few tens to to a few
hundred watts to big speakers.

The biggest user of power is the hard drive and display on players so
equipped.