Missing the point. Why does a class have to be starkly limited in combat role.
Which class is "starkly limited"? Classes have things they do well and things they do less well. But it's possible to heal with any class (although leaders will always be better), to tank with most classes (Invokers have it tough), to do damage with any class, and to force bad choices on the enemy with any class. The role indicates what they can do best, not their absolute limits.
Why do classes even need combat roles? Why does everyone have to be a combatant?
Because this is
Dungeons and Dragons. If it were Courtiers and Merchants it would be a different game. And not everyone has to be a combatant. You can play The Load if you like - it just takes dumping your primary stat. And sit there like a lemon while the game is in combat (a significant proportion of the time) and your character is hiding under the table. Or you can simply refuse to use your powers.
Gygax wrote a thief, not a rogue. Also, why do we need to slavishly follow design decisions over thirty years old?
We aren't slavishly following it. If we were then the rogue would be hard coded into his own mini-game.
Ah, the old 'just re-skin it' argument. Why should you have to re-skin it?
Because the alternative is to make everything vanilla out of the box (so you aren't reskinning so much as skinning). Or you need a literally infinite number of feats. As you seem to be requesting.
Why can't choice of faith, skills, feats, and abilities have the same effect?
Because none of those deal with the character's overall approach. Which is what Class indicates. Which is to open up design space without warping the game into a pretzel and make it easy to build competently with minimal skill. (Seriously, a 4e Shaman would be near-impossible in a pointbuy system.)
You can play classless. I'm a fan of both GURPS and Spirit Of The Century. But having classes brings its own advantage - I'm also a fan of 4e and Feng Shui. Classed is easier to get into and set up. And if done well it doesn't rule out a lot of design space.
And an Invoker doesn't fill the mark because I said a paladin, not an divine wizard.
OK. A greatweapon fighter with the Paladin multiclass feat. He's a Paladin and does a hell of a lot of damage. And then he's God's Vengeance wielding a martial weapon. And that's only if you need heavy armour as part of your core concept (Thaneborn Barbarian MC Paladin fits what you want even better if you don't mind Hide Armour, and then there's the Avenger).
What point? That you want infinite flexibility in character generation. And a pony?
The point is that a good class-based system (and 4e is one) is a hell of a lot more flexible than you seem to think.
Who said anything about housecats. There's a big gap between that and not having any combat focused abilities.
Pre-4e an average first level wizard who had no combat spells available could be beaten up by the average housecat by the RAW.
And if I don't want a boatload of semi-magical combat powers? I said non-combatant. Also this seems needlessly complex and fiddly.
You want to play a non-combatant in a game of
Dungeons and Dragons. Are you also complaining that
Librarian: The Return makes it hard for you to play an illiterate PC?
OK. Non-combatant recipie: Put your sword down and only use weapons you aren't proficient in.
All game worlds will have a system to work. It's human nature.
So not only do you want a classless system, you want a specific system to each gameworld. And the homebrewers need to come up with their own? Fortunately 4e is a bit more flexible than that.
Again, more build fiddling. What if I want that at 1st level?
Then you want to be incredibly knowledgeable about everything at 1st level. (Although starting with six out of seven trained skills from that list should be possible for any bard - and Streetwise isn't necessarily part of the core concept). What if I want to be tough enough to beat up a dragon single-handed at 1st level?
The merchant with no combat abilities beyond swinging a sword (or shooting a bow) and harsh language.
... is playing the wrong game.
Seriously, it sounds as if your objection to 4e is that it is Not GURPS. And that it doesn't have rules for everything you can come up with.