There are a few situations in which compensating developers are very
useful, but generally I find them to be a crutch for incorrect
exposure.  Any compensating developer will bring the highlights down
considerably when compared to a "standard" developer that gives a
straighter curve.

Many developers using pyro as the main developing agent give strong
compensating effects -- and it's not inappropriate to use them for
this purpose.  But there are considerable drawbacks, including the
difficulty of measuring the actual effect of the image stain on the
final print -- you need color curves for the paper and,
if you really want to get it right, curves for all three of exposure/silver
density, exposure/stain density, and stain density/stain color.  You'll
have to generate all of these yourself, as they're not available for
monochrome materials from the manufacturers -- and note the enormous
number of variables involved.  I want less variables in my darkroom, not
more, and I certainly don't want to go solving 6-variable equations to
figure out how to adjust my exposure or development times.

The difficulty of modeling the actual effect of image stain on
the final print in a concrete, mathematical way has led to some rather
notorious confusions, e.g. the promotion and then withdrawal of the
alkaline post-fixer soak for PMK, which is now generally thought to
increase only overall image stain.  Since the general effect of this
stain will be to decrease contrast and increase printing time with the
VC papers most printers now use, there's an obvious appeal here: most
shooters do, in my experience, tend to underexpose and overdevelop
their film a lot of the time.

But note that one could have achieved exactly the same result -- since
all that result really was was a dark yellow base fog -- through proper
exposure and development without the exotic developer.

Add to that the questionable archival status of the stain from most
staining developers -- at the very least, it shifts color over time --
and you have a kettle of fish I don't really want to eat, at least
not for lunch every day.  If I have some film I know was shot in
conditions of extreme contrast, to the point that very dilute
conventional developers won't help much, I may mix up a liter or two
of PMK or some other exotic -- but certainly I do not want all those
extra variables in my day-to-day workflow.

And certainly I see little to no reason to use oddball developers with
purported developing agents like instant coffee in them just because
they happen to stain the film emulsion.  So does India ink.  So what?
You won't catch me pouring that stuff into a tank in my darkroom, after
all.

If you want heavy base fog and low contrast for some reason, you could
always pre-flash your film.  It seems a very, very curious reason indeed
to choose one developer over another.