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As I said, it's a wild guess, but the basic reasoning is that each of the
following seems it should be significantly stronger than the next:

Wazir > adding null-move to King (endgame value) > adding null-move to King
(average value) > triangulation on every piece in your army > triangulation
on a single piece

Empirical testing of the switching weakness is a nice idea, except that I
suspect that its effect is much smaller than all sorts of other effects
that we don't know how to control for.  For example, if you compare NW to
NF or ND (as Robert Shimmin did earlier in this thread), then NW is
switching while the others can triangulate, but that's certainly not the
only difference (and in fact, Shimmin's test indicated that NF > NW > ND,
which proves that *something* has a larger effect on his test values than
switching does).  Betza suggested that the NW's aptitude for perpetual
check may be relevant, and also the NF's ability to escort a Pawn unaided;
I think someone else suggested the NF gains because a Pawn cannot make a
stealthy attack against it.  Forwardness and mobility also differ between
the listed pieces.  Speed may also be an issue, since it takes a N three
moves to simulate a W move (in an open position), but only two to simulate
F or D.  And there's probably another dozen factors that each MIGHT be
more significant than switching.

So I can't imagine how you'd construct a *controlled* test of
triangulation/switching without a much more comprehensive theory of piece
values than we currently have.

Investigating the value of a null move should be easier, and it obviously
must be at least as valuable as losing a tempo to triangulation, so that
might give an upper bound (though perhaps a very loose one).  It wouldn't
tell us if switching is a disadvantage for some reason we haven't thought
of, though.