Well that sent me on a search where I found this from Patrick Gainer on a thread about a "sort-of lith developer":
http://www.photography-forums.com/threads/hydroquinone-stains.93280/
" Hydroquinone used as in your formula is a tanning-staining developer in
the class of catechol. A small amount of sulfite will eliminate the
staining, but the staining is what gives it a warm tone effect. The
stain is redder than pyrogallol's and not as resistant to sulfite. The
stain is a dye formed when hydroquinone is oxidized, and it is quite
permanent AFIK."
This isn't the final word by any means, but since Patrick seems to have been the modern re-discoverer of the staining HQ developer it has some value.
It's a shame Patrick can't participate or do darkroom work anymore. His negatives from the early 2000s might be the "oldest" hq stained negatives that could be checked for their permanence.
Maybe I'll toss out this alternate theory: Could it be the stain color that renders it less popular than other staining developers? This will surely affect it's usefulness but it's too difficult of a thought experiment for me to carry to completion.
AFAIK Hydroquinone is used in lith developers with almost no Sulfite and at rather high pH. I am surprised that nobody noticed any toning properties during all these tests and experiments with lith.