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George, you've got some things going here that, naturally enough, I don't
fully agree with. Let me start by taking issue with the following quote:
'Disparagingly, 'pseudo-compound' fits also because of improbability
that movements combining powers at opposite extremes, namely leaper and
one-path slider, could be very effective within one piece. Hence their
unpopularity.'

Contingency, historic accident, is a poor base on which to build an
argument of inevitability, and buttressing it with an unsupportable slight
does not help convince the skeptical reader. That a piece is worthless, or
at least worth little, if it is not in current use by millions of people,
is at least historically demonstrable as false. New pieces do arise and
are not always popular at first. Think of the genius who first invented
the knight move; and then wonder just what his/her friends thought and
said the first time that crooked jump move was used on them. How popular
was that piece in the beginning?

The piece I wish to consider is the combination dabbabah-wazir [DW]. Let
me hasten to add that I don't expect this piece to take the place of the
knight in 100 years, or anything close. But I do wish to examine some of
the potential for this apparently unprepossessing piece, very specifically
because it combines a leaping and a non-leaping component. The DW has as
its basic moves a 1-square slide or a 2-square jump. If allowed to use
both halves of its move, it leaps and steps 1 to 3 squares, an inclusive
compound piece [DHowe 'A Taxonomy']. If the piece instead repeats its
basic move once or twice, it becomes a limited rider and may move up to 4
or 6 squares. The 3 step DW rider is an interesting medium-range piece
that I have not seen examined in any games. I don't have a real
combination leaper and multi-square slider there, but the piece may leap
once and step/slide 1 square twice in its move, or even slide 3 squares as
its move. Will this piece do as a counterexample, George?