So are the PCs, which is the very root of my whole point here.
No. they aren't. They are the focal point around which the game, in a mechanical sense, revolves. No matter what their background, history, or purpose, the game is, ultimately,
about the PCs, not the NPCs. Detailed options that are available to them on a regular basis are superfluous or extraneous when applied to NPCs who are only going to be on-screen for a limited amount of time, and powers and abilities that might be exciting and engaging in a limited quantity (such as the hypothetical encounter with the shaman who can heal and sling fire with equal ease)
will prove problematic in the hands of people who are on-screen all the time and have those abilities as a normal part of their problem-solving repertoire.
If the PCs are not representative of that teeming mass then they're either alien to the world or are truly special snowflakes. The former can be cool if only done once, while the latter just ain't the way I roll.
This is a Story take on what is, ultimately, a Gameplay problem. You can use flavor to justify
any kind mechanics. You
can't do the reverse and have it reliably work, and the 3.x era was a prime example of
why. This has nothing to do with the PC's fictional positioning, and everything to do with with the PCs-as-game-pieces. This is a game design-level issue, and it's present in pretty much any RPG you care to name, not just D&D. You either need to stick so much detail on an NPC that they become cumbersome to use in the moments they're on-screen, or you use a different system for building them, which has the flexibility to add what you like but that very strength means they have access to abilities that PCs don't get.
While I get this in principle, a few points:
First, that bolded claim is likely to go over like a lead balloon with some here.
That's a "them" problem. Objective reality doesn't care about their feelings on the matter.
Second, while I might in theory be a part of a "team-based tactical squad" (shudder), both as player and character I'm also a free-willed individual who may or may not always feel like following orders or sticking to plans.
And this has no bearing whatsoever on the objective facts of your character's place in the game. The most free-willed pawn in Chess still only gets to move one square forward at a time and only capture pieces diagonally, as much as it might want to sulk about that, and it can't be anything different unless and until it reaches the end of the board and gets promoted.
Granted, RPGs allow their game pieces a lot more freedom than that, but at the end of the day,
they are still pieces, not people.
(This, incidentally, is why I also reject "it's what my character would do" as a defense for wangrod behavior at the game table. The "character" is nothing more than the player's agent in the game world. The player is choosing the character's reactions, not the other way around, and any claims to the contrary are just attempts to deflect responsibility for being a wangrod. The player is the one with agency, not the character, and they've chosen to exercise they agency to harm the game experiance of everyone else for their own selfish reasons, and that's generally unacceptable.)
Third, my question "Why can't I play one of those Shamans?" wasn't meant to imply just tacking those powers on to my existing character but more a) why isn't that class in the char-gen guide and b) why can't I drop my current PC and take one of those instead (i.e. switch one set of limited tools for another)?
I can spin a bunch of Watsonian nonsense to justify my decision, but the Doyalist reasons probably are:
1) This is not a player option because the designers had niche protection goals.
2) This is not a player option because the designers had character balance concerns.
3) This is not a player option because the designers had Watsonian world/setting reasons not to include such. Whether this is valid is going to be up to individual interpretation.
4) This is not a player option currently, but isn't unbalanced or oversteps niches too badly, and the designers either haven't thought of it or are waiting to put it in a different supplement to get more of your money down the line. Or a Third Party designer has cobbled something together that the GM feels comfortable adding to the available options. Or the GM decides to home-brew something.