Some scattered thoughts about various topics discussed here:

*Depending on how deep you wanted to dive into the splat, 3.5 had a number of different "skill-monkey" classes that fit into different archetypes; it's just that most were given additional benefits (spell-casting or precision damage). Factotum from Dungeonscape was the purest option, given that its class skill list was: All. But Rogue worked perfectly well for the role and Scout was basically Nature-Rogue. Archivist was your Knowledge-skill monkey. But once again, each of these classes also fit a specific archetype, which brings me to:

*Generic vs. "Baggage" classes. It really feels like the overriding trend in D&D over the editions (and especially in 5e) is the move away from "generic" classes or classes without "baggage." I think it was Chris Perkins who was lamenting the lack of a true identity for the Fighter. They had made the class too generic in their eyes. I personally believe you can point to a lack of clear and consistent identity is the reason why the Ranger is such a contentious class (and thus a bit of a mess conceptually in 5e).
This is because D&D is emphatically not a generic fantasy role-playing system. D&D makes a number of basic assumptions about the nature of its fantasy worlds. Sure, some established settings have unique twists on those assumptions, and obviously there's no stopping home settings from tweaking those assumptions. There is no design space for an official "generic holy warrior" class in D&D because to be a holy warrior in D&D is to be a Paladin. Or, you know, a Cleric, or a Fighter with the proper background and/or feat(s).
That's not to say that there isn't demand for that and other class archetypes you mention. I'd be interested to see homebrew attempts at a different kind of holy warrior, or a different kind of skill monkey class, or animist, etc. (I must admit to not understanding at all the desire for a non-adventurer adventurer class; and I've played multiple 3.5 PCs that were functionally useless in combat). I wouldn't personally be happy if those classes were generic but to each their own. But I think D&D, and especially 5e, has a very clear design principle regarding its own classes, and that is "not generic". Classes have flavor; they have character; they have a clear identity. They have, by design, "baggage".

*D&D has, through much of its history, appeared to emphasize the combat pillar because its core design and rules emphasize combat. There are specific rules for combat that are basically universal to all D&D tables. In contrast, the rules for exploration and social interaction are much more abstract, mostly resolved through the game's most basic mechanics. I assure you that if 5e had rules for exploration that were as in-depth and unique to its sphere as the rules for combat, it would probably have just as important a role in the game (and class design and abilities would likely reflect that shift in emphasis). 4e attempted this with skill challenges, but it made two critical mistakes: the shell of the skill challenge mechanic was broken, and it tied into an aspect of character creation/development that the edition had deliberately simplified. A well-designed skill challenge system using 3.5's skill mechanic would likely have been much more successful; especially if the skill challenges had major differences based on challenge vs. environment (exploration) and vs. individuals (social interaction). But then you're starting to into rule bloat and being too complex. But simplifying rules for combat would be killing the sacred cow.