Which goes back to my earlier post: at some point EVERY class is an artificial construction of background, skill and theme. Even fighter and wizard (which we can argue are the backbone of classes; one's good at combat, the other casts spells) in the end are nothing more than a background (I studies books/swords) and talents (I cast spells/I swing swords) and theme (I learn spells from a book/I use heavy weapons and armor).
To a matter of degree? Sure. To the same degree that the current 5E models Class-Background-Theme? Certainly not.
Which is why reductionism is a slippery slope. If a monk (with its oddball mechanics) don't qualify for a class, what does?
So, because you choose to engage in a textbook Slippery Slope Fallacy taking any sort of reduction or compartmentalization approach to handling traditional classes as builds is BadWrong?
I respectfully disagree.
Does an Assassin or a Barbarian?
That entirely depends on what your definition of "Class" is. If Class is a large tent of options around some core backbone of distinct rolls (using Fighter, Rogue, Magic-User, and Cleric as cardinal points) without mandatory associations to Background or Theme slots then no, they certainly don't fit that criteria. If Class is a fully-supported combination of level-based abilities from a Super-Type (like the cardinal point Super Classes) plus a particular Background and Theme then yes, certainly.
That's probably the biggest impediment to the discussion and the design going on at the moment - confusing "class" with "build," just because that's what 1st Edition did with some things. It isn't like Barbarian, Paladin, Druids, or Ranger were classes either - they were sub-classes. In 2nd Ed you had "kits." 3rd Edition lost that in favor of patchwork multiclassing and Prestige Classes.
Does a Druid or a Ranger? Does a Paladin or a Bard? Does a Rogue or a Cleric? Does a Fighter even? At what point do we decide X is a class and Y is a theme/background?
When it has a distinct niche (for example: Warrior, Holy-Man, Magician, Rogue) that doesn't so severely constrict your Background and Theme.
I'm horribly leery about making any former class a theme now, since the standard for doing so is the arbitrary "I don't think it deserves to be".
The standard, while nebulous, should not be "because I'm not a fan of that class." It should be "I can cleanly construct it out of balanced modular components (that have multiple applications) without a ton of hassle."
- Marty Lund