My own experience listening to AM-HD is I thought it was somewhat an improvement in sound quality depending on the station - certainly a lower noise floor with HD. Also when Radio Disney still had a bunch of HD AM's running, I found music better than news/talk on HD. Any digital artifacts were not as noticeable to my ears. Station's with good analog coverage seem to do best with it (like KMOX mentioned earlier, WTIC, WPHT, WBZ when they ran it). With WINS and WCBS around NYC it did seem to cut in an out of HD a lot falling back to analog in my limited experience driving around Manhattan. It seems to work better once you get out of the city a bit for some reason (maybe HD is more affected by the tall buildings?)
My experience with the FM-HD 2 and 3 signals is not great. Cuts out too much and when it does it doesn't fall back to analog - just no sound - so I'd rather stay on AM. If HD radio supported failback from and FM-HD 2 or 3 to an analog AM that would be an interesting but it doesn't.
During the CBS radio days, when they went to the 8khz analog mode with their HD-AM's that made a big improvement in the analog quality on my radios (mostly units with wider bandwidth). Many AM's were running to AMAX standards (10khz) in mono or stereo right up to when AM-HD became common but then some fell under corporate mandates (as I understand) to conform to the HD frequency cutoffs even if not running HD. At one point I think Clear Channel/iHeart mandated 5khz cutoff on all stations but seems that is more relaxed now. Also my experience was the CBS stations moving to 8khz mode eliminated the self inflicted digital noise on their analog signal.
Generally if AM sounds bad on your radio it is your radio. My Ford vehicles have generally had decent AM sections. Units from the late 90's and early 2000's - especially those with AM stereo support - are good out to the AMAX specs and sound great. My last GM car - 2008 model year - the AM was pretty narrow and not that great sounding. At home I have a Denon wide bandwidth tuner that sounds great. My Yamaha tuner with HD capability is ok but not as good on AM analog. I have an aftermarket Pioneer HD capable radio in one vehicle that has a decent analog AM section - better than the GM unit. Adjusting the tone controls or equalizer if the radio has them can help.
If you want to hear great sounding AM - find a wide bandwidth, AM stereo tuner (like in the Ford vehicles from the late 90's) and listen to WJIB in Cambridge/Boston MA. Spectacular sound and pretty good coverage considering the transmitter power.
I was hopeful when HD came out it would help AM especially since with it being an update for both FM and AM, it would tend to just come with new radios more than the last attempt to help AM (AMAX and C-Quam) but between the low adoption, competition with streaming, end consumers not needing it for FM since FM sounds fine already and has a data stream with RDS it just hasn't taken off that well. Add in the expense of licensing for stations using it and extra maintenance of equipment for thin engineering crews the future does not seem that bright for it.