"No other classes fits in my image of D&D"
"I just can't think of any other classes."
Mostly a combination of these two, for me. I don't have active opposition to the idea of adding new classes. I
do think there's a tipping point in complexity, though, where a whole new class becomes splitting hairs and the length of the menu becomes more of a liability than a benefit. I think about 15 classes, with about 5-6 sub-classes, each, is about right. Throw in about a dozen generic backgrounds and another dozen (or two) per setting, and you've got a nice way to support a lot of concepts. A few feats makes it even sweeter, but they're optional.
Using the menu metaphor, some class concepts could be seen as having different entries depending on whether you want a soda or a glass of wine with dinner -- or even whether you want seasonal vegetables vs. a baked potato. I say, use the option to drill down where it makes sense. That much should be straightforward and easy to agree upon, IMO. The conversation gets interesting when people can't agree on what choices belong at what level.
For example, my vision of what a Psion represents (folks with innate supernatural powers) is reasonably compatible with Sorcerer. If you added a way for the Sorcerer to not have to
cast the spells (innate magic that requires specific VSM components? I don't think so), I'd be totally fine with it. For others, psionics is clearly something wholly separate from magic and the Sorcerer is just not acceptable.
My post confined itself to the question as written: "What
classes do
you want written for 5E?" (Emphasis mine.) I intentionally excluded anything I'd do as a subclass, feat, or background. I also excluded existing classes that I'd like to see rewritten (Sorcerer, Ranger). I also left it to what I, personally, wanted covered.
I can go down your list, though, and give specific opinions:
Truenamer (flavor and mechanic) -- Interesting concept. I'm not sure it plays well with the rest of the D&D framework. I don't yearn for it, but I'd at least check out an offering.
Binder (mechanic) -- I actually really liked the 3.5 ToM version. In 4E, the Warlock took some of his stuff. In 5E, since I don't like the Far Realms, I just use the GOO Warlock to represent someone who gains power from a vestige. I'd check out a fuller implementation, but I'm pretty happy with what I have.
Shadowcaster (mechanic) -- Don't recall enough about it to opine.
Dragonfire Adept (flavor and mechanics) -- Never heard of it.
Warden (flavor) -- Was this the 4E Primal defender? I don't do much IMC with what would be "Primal", so I don't have a direct interest. My gut says that the field is crowded enough with the Barbarian and Ranger. Since I'd happily drop the Barbarian and would love to see the Ranger distance itself from Druids, I sure wouldn't say no.
Warlord (flavor) -- This is one I definitely see as overly specific (separate entry for potatoes and veggies). I liked the class in 4E, but
what I liked about it is sufficiently handled by either the Battle Master Fighter or the Valor Bard.
Archivist (mechanic) -- No clue what this is.
Incarnum classes (flavor and mechanic. -- I, personally, strongly disliked the whole concept and have no interest in them. That said, I'm not sure any existing classes would handle them well.
Psionic classes (flavor and mechanics) -- Touched on this, above. I'd prefer a formal 5E psion. I don't think what WotC will deliver fits my vision, but whatever.
Artificer (flavor) -- Yes. This can't be done as a subclass, IMO.
Alchemist (flavor) -- IMO, this could be implemented as an Artificer subclass.
Martial Adepts (mechanics) -- Not sure what you mean, here. For one definition, I can see Monks fitting the bill, at least in the same way that the Sorcerer could be a Psion. If you mean 3.5
Tome of Battle, then I'd actually say it should be avoided. It was an interesting concept, but was really just a trial run at the 4E power structure. Would I like to have fighting schools? Yes, but I think it would be better done with one of the other dials.