It's not that I don't understand that perspective, it's that I think the expectations you're outlining are unrealistic. If you're playing a roleplaying game and your expectations are centered around your mechanical effectiveness, there's something wrong, regardless of whether those expectations are met.
If we were playing a modern rpg, we would never expect that a doctor character have the same mechanical usefulness as the hospital janitor. In fact, we wouldn't even expect that every doctor be the same. That doesn't stop some people from wanting to play the janitor. But in D&D, we already have unrealistic and very harsh strictures forcing everyone to essentially play professional adventurers of roughly equal effectiveness. That this isn't more than enough to satisfy those expectations on account of some relatively trivial and nuanced (and entirely justifiable) variations between character types is pretty mind-boggling to me.
That, and the other problem would be if you don't understand that you're only a few relatively small playstyle differences away from a scenario where the "Angel Summoner" is a cute distraction for the badass dude with the sword.
And the notion that my expectations are unrealistic is the problem here. They're not. For D&D, which is the game we're talking about, right?
Roleplaying games are about several things, but let's divide them neatly into two parts by the name: roleplaying and game. Two parts. I love the roleplaying aspects to RPGs, and play in a lot of games where that's the most important thing that we do. The 4E campaign I just finished up was largely about political maneuverings in the takeover of a country, and we'd go multiple sessions with no combats. No problem with that. (As an aside, the 4E system had no problem with that either, nor would I expect that any edition would). The roleplaying part of RPG doesn't have or need rules: you tell the GM what and how you want to do something, and most of the time it just happens. I daresay that 90% of the things we talk about doing in an RPG don't need dice and just happen.
When we get into the other part of the term, the game part, mechanics are important. The Next designers have spoken about three pillars to the game, and this is one of the best ideas they've brought forth in my opinion, since it's giving us insight into what the game is about. D&D is different from other games in that they'll likely have different pillars and focus on different things.
So Next, in theory is centered on three concepts: social encounters, exploration and combat. That's telling us what are game is going to be about, and the goal (again, the goal the designers have stated) is that each character will have something to do in each of those areas.
What that tells me is that if I pick a basic character, they will have something to contribute to each of the main parts of the game. I might be better at one than the other, but the expectation is that I can do something useful in each part. How do I do that? Mechanics.
So if I'm a fighter, to give the rogue a break, and I find that I can't contribute to the group when we're exploring or socializing, I have the right to say "what gives here?" It's not poor playing, it's not unrealistic, and it's not a sign of being an immature roleplayer. It's actually bad mechanics, given that we started with the premise that characters can do something in a core element, and find that game doesn't let us in practice.
As you say, in D&D there is an expectation that you're playing a competent adventuring person. That's the default for the game. D&D really isn't intended to be a game where you play the equivalent of doctors and janitors. If you try to do so, you will be disappointed, and here's the key: it's not the game's fault. The game told you what it was about (three pillars, right?) and that you would be able to do something in each of those parts. What would be bad design is if your expectations of being able to contribute in each part of the game weren't met.
There are games where you have janitors and doctors interact and no one seems to mind. I think the zombie survival genre is the best example. In that case, I'd expect the janitor to be just as useful as the doctor if not more so, outside of when people getting hurt. The thing is, healing injuries would not be, in my expectation, one of the core "pillars" of the zombie survival genre. I'd expect that
keeping the group healthy, overall, would be. The doctor would contribute by medical skill, while the janitor would (for example) scrounge for supplies. Different actions, but part of the same overall game pillar.
That would make for a good zombie game: the two characters are different, but each one contributes to the core parts of the game, just in different ways.
In D&D, this means that each character does something to contribute to combat. That doesn't necessarily mean "a lot of damage," but they each get to do something during that part of the game, as with social and exploration encounters. I don't think that's a radical notion or anything.