what speakers demand high end electronics

ALL speakers require high end electronics to sound their best. All sources require high end preamps to sound their best. All amps require high end speakers to sound their best. All anything requires all high end everything else to sound their best.

I can't believe I just took the time to write that. That is the end of this thread. There can't possibly be any other answer.
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Sorry Herman, I have to add one more thought. To sound their best, all speakers need to be fed by well matched components. A system put together with a bunch of high end mismatched equipment will not make MUSIC.

The question stems from Harbeth speaker designer Alan Shaw's statements that his speakers can do just fine with inexpensive amps. I know there are speakers out there that owners say would be need very fine electronics to make them work. So thanks for highjacking my little bit of entertainment with my hobbie.

If a loudspeaker has a benign impedance curve, it will usually sound pretty good with modest electronics provided the efficiency isn't extremely low or extremely high. The latter proviso is somewhat counter-intuitive, but often very high efficiency speaker sound their best with specialty tube amps, which can get pricey (but sound really good).

As a practical matter, an enormous amount of money can be spent on a quest for "the best". Most of us would run out of money long before we get there, but fortunately most of us are also quite happy with "great in the areas I really care about, with the inevitable compromises relegated to areas I don't".

Duke