One of the problematic design decisions that went into AD&D 2nd Edition was the loss of the Monk. It was admittedly a problematic class in 1E, pitifully weak at 1st level but quite powerful later on, and it was, as we say, not quite as thoroughly baked as most of the rest of the classes.
However, the far less playable Bard was not only retained in 2E despite being clearly optional in 1E, it turned into a quite serviceable and useful class. The Assassin, it is commonly assumed, was omitted as part of the effort to made D&D less controversial — an effort which cost us demons and devils as well, at least for a while. I surmise, then, that leaving the Monk out was left over from Gary Gygax’s aborted plan for a second edition, wherein monks and other Asian-inspired character classes (like those from Oriental Adventures) would be shunted into their own book.
This seemed at the time to perfectly reasonable on the face of it. D&D was considered, for a long time and by a lot of people, to be a fairly generic fantasy in a lot of ways, despite its reliance on, for example, the relatively arcane (har, har) Jack Vance’s tales of the Dying Earth for inspiration for its magic system. As time’s gone on, though, and we have seen more different types of fantasies, particularly those varying from the old standards of Tolkien, Moorcock, Anderson and Howard, and as Vancian magic has become more and more an outlier, it’s become increasingly clear that D&D is in no way generic in any sense. It represents, in fact, a very specific type of fantasy, one inspired by the above-mentioned masters but also deveoping its own tropes and conventions… and even, in time, exerting some influence of its own on fantasy outside itself.
The Assassin was another problematic class. What the “assassination table” actually meant at the table was hotly debated at one point. Personally I would, in retrospect, treat it as a way of resolving assassinations which happen more or less entirely off-camera. There was no real infrastructure, much less mechanics, for handling the Assassin’s work leading up to an assassination: the casing of the target until his moves were predictable, the study of his defenses of guards, the acquisition of untraceable weapons, and so on. (Gygax’s Assassin is undoubtedly inspired by Leiber, but for an excellent depiction of this kind of thing in a fantasy context, by the way, see Steven Brust’s Jhereg.)
D&D’s Third Edition understood that these two classes were an indispensable part of the D&D mythos, and included both; the Monk as a class in its own right, and the less obviously Assassin as a prestige class. And it included a revision of the fan-favorite Barbarian from Unearthed Arcana, although the other creations from that volume, the Cavalier and Thief-Acrobat, didn’t make the cut… I suspect because no one really knew what to do with them or had a reason they should be in the game and distinct from the other classes.
There is probably room for specialist Magic-Users along the lines of the Illusionist, although the precedent for such is far less clear, though not nonexistent. But there’s three “missing” classes that have been part of the mainstream of D&D for good chunks of its life, but which are missing from some editions. Classes, I would say, that any self-respecting clone ought to make provisions for. Or any upcoming new edition, if it’s trying to be a unifying revision that brings everyone back together into the same game system again. You’d include the Bard and Illusionist, too, for completeness. That’d be a nice class selection.