In areas where the playing is for dance-derived roots or traditional folk music, there is a strong history of the so-called "true musette" or MMM sound in the musical genre, and as at least an option in the accordion registers. That goes for French, Irish/Scottish, Tex-Mex, and more. Over the decades MMM came to be looked down on, and there was a move to thinner tremolo or musette, or even to dry tunings with no MMM.
But MMM as an element in some of these music traditions hasn't disappeared. Actually, very recently some players in the Celtic genres seem to be getting back into MMM as a sound option. If you play world music such as French musette or Irish or Scottish and you're motivated to lug around a 4-voice, there's little use for an H reed, whereas it's cool have the choice of going MMM or MM whenever you feel like it. (Cajun it's different--Cajun one-row bisonorics have an H reed in the arsenal, but they are kind of sui generis because they are tuned differently from strict concert pitch, and fiddles have to tune to the accordion because of this.)
I recently saw a blurb on a post by an accordion dealer in the UK that purveys to a lot of Irish and Scottish players, noting that of late there's been a lot of interest in using the MMM to have two MM 2-voice choices tuned sharp in different degrees of wetness. So, the player might set one at MM +7, or even MM +4 for that "dry swing" currently in vogue with some Irish or Scotth players. And then set the other one at MM +10 or +12. And use them together MMM (all in tune with each other, of course), when you want a stronger voice.
But very recently, the LMMH option seems to be having a "moment" or a resurgence, and not only in the high-end classical or jazz use, 25 to 30-pound cassotto realm. It's currently not unusual to see non-cassotto, more general purpose boxes offered in stock by dealers in two configrations, LMMH or LMMM. Personally, I don't believe any listener or audience member would know or care one iota whether the player has an H reed their sound, but the H reed is kind of "back" at the moment.
I was recently watching a pair of gorgeous 37/96 Scandallis in "olive ash" wood at Liberty for a while, a pair of siblings offered in LMMM and LMMH. It was kind of fantasy porn, as I don't want a 19-pound 4-voice, but if I did, those were the stuff. I just saw the LMMM has vanished and the LMMH is the last one standing. Make of that what you will. For the record, I would have gone for the LMMM too. I love a thinner MMM, say, -7/+9 or 10.