There is nothing in HD radio that improves coverage. In fact the FCC keeps the power of HD channels to around 10% of the station's primary carrier. So it wouldn't help the station cover the market.
Overall coverage, maybe not, but at -10 dBc (the 10% of analog power level that is the maximum the FCC allows), current transmitters and encoders put out a signal that's very usable out to any given station's protected analog contour. The original -20 (1%) level was indeed way too low, but -10 tracks very closely to useful analog coverage.
A lot of the complaints of HD fading out before analog or ping-ponging back and forth were real problems in earlier generations of HD equipment, but they are problems that have been largely solved by higher power levels and better encoding. I suspect many who still repeat those complaints haven't driven around a major market using newer generations of transmission.
And in areas like SF or Seattle that are prone to multipath, I've found that a -10 HD signal can be much more robust in the car than analog. I had that very experience today - driving into NYC along the Palisades, WFUV in analog was a multipath mess, but it quickly locked into HD and stayed locked, and became a much better listening experience heading to the city.
With the sheer number of HD tuners that have been placed in dashboards in the last 15 years (heck, there's one in my wife's janky 2013 Prius that's already at its end of life), I suspect there are a fair number of listeners out there benefiting from nice clean HD reception without all the picket-fencing.... and for them it's just "radio" and they may not even know they're hearing HD.
(Edited to add: it's easy to forget that the first generation of HD equipment, all those awful BE boxes, Nautel's early stuff, and so on, is already going on 20 years old. In large and medium markets, that means most of it has already gone end of life and been replaced by much better, newer rigs. Nobody builds space-combined sites anymore, or worries about high- or low-level combining or heat dissipation. You buy one integrated box from Gates or Nautel with one output to the antenna, and it just runs. The difference between HD transmission technology in 2003 and 2023 is even more dramatic than all the ways FM improved from the 1960s into the 1980s.)
Any of the bigger players, whether it's iHeart or Audacy or Cumulus or public radio*, uses -10 dBc HD as a standard part of any new build or upgrade. I can't think of the last time I saw a large-market station do a build without current HD.)
((*yes, Paul, we know your particular NPR station will never...))