Yes, “cozy” has become a marketing term rather than a good descriptor, and the modern cozy resembles the classic mystery the way a PT Cruiser resembles a car of the 30s.
Many writers dislike the term cozy because it is almost invariably applied to women authors. This is good in a way, because women have always bought the bulk of mysteries, but it also serves to lock out male readers. Cozies are defined by their worst examples, as Theodore Sturgeon once said about science fiction. They are feminine and fluffy and silly and bloodless and don’t have big masculine toys like guns and bombs.
Though the word is new, the separation isn’t. Dashiell Hammett and the rest of the writers at Black Mask magazine deliberately wrote for a male audience who wanted mysteries to reflect the deadly world of the mob and corrupt police that grew up under Prohibition rather than upper class killers who used undetectable exotic poisons. As Chandler said, “Hammett gave murder back to the kind of people that commit it for reasons, not just to provide a corpse; and with the means at hand, not hand-wrought dueling pistols, curare and tropical fish.”
Even the members of the Detection Club, who set the rules in the OP, were trying to get away from some of the worst excesses. Unfortunately, their “decalogue” was superseded by S. S. van Dine’s 20 rules, which were partly sensible and partly looney - good writers of the 30s and 40s broke his “rules” deliberately and created some of their best books by doing so.
The backlash to the classic mystery resulted from a change in society. After WWII nobody believed in amateur detectives. Mysteries were supposed to be solved by professionals, who were experts - police of all varieties and private eyes. Spies, who were the most professional of all, became huge in this period. Even in the Golden Age, it was hard to make amateur detectives believable, and few of the Detection Club members wrote about true amateurs. Chesterton did with Father Brown and Sayers with Wimsey, true, but these men did have professions - one was a priest and the other a peer of the realm. Look at the others’ famous detectives: Poirot was an ex-policeman; Croft’s Inspector French a current policeman; Bailey’s Reggie Fortune was a doctor who worked with the police; so was Freeman’s Dr. Thorndyke; so was Rhode’s Dr. Priestly. You have to go to Christie’s second character, Miss Marple, to find a true woman unemployed amateur. Women had to be amateurs because they couldn’t be professionals; men had to be professionals because it was unmanly not to be one.
That’s what drew women into the mystery field in recent decades - the chance to go against the male professional with amateur females. Not surprisingly, people saw the deliberate differences and put the subgenres at odds with one another, emphasizing the ends of the spectrum. There are plenty of books in the middle - Donald Westlake wrote the most masculine of hardboiled crime novels in his Parker series and also wrote as many light & funny comic crime books about amateurs who get swept up in a plot - but people like putting labels on things. There’s an equal division between science fiction “male” and fantasy “female” and it’s equally removed from reality.
Sorry. I go off too long on this stuff, but I find the history fascinating in what it says about things you wouldn’t think mere mystery categories would tell you.