I tried a direct response, but my demunging wasn't crafty enough for
your email's reply-to.
The documentation for TransformationFunctions (with which I haven't
played, but wish I knew about far, far earlier) indicates that if the
user includes a list of transformations to try, only those are used. It
seems that it gets at the problem of strange outputs from just the other
direction of what you're suggesting.
I would guess that if a user knows exactly the form she wants, and can
express this correctly in a function, the built-in
TransformationFunctions would be more appropriate. However, as you say,
often the form the user wants isn't predetermined, but the user
certainly knows which forms he or she don't want, especially after
seeing them returned by Simplify.
My final thought is that in its implementation, your method would have
to include some transformations of the form that TransformationFunctions
requires; otherwise, Mathematica would just have a restricted set of
transformations from what it usually tries, and will, almost always,
return the original expression, unevaluated. Of course, I don't know the
code's true structure, and so can't be sure.
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