"Fighter" and "rogue" and even "wizard" don't give a newbie much to hang a character concept on. Everyone fights, nobody follows the laws, magic is something every PC eventually uses to some degree, and none of that speaks to who your friends or enemies are or why you might go on adventures. It's open-ended and nebulous.
My very first official character was a Wheel of Time character. There were classes like Noble (tied into the political games specific to the setting), Algai'd'siswai (specific warriors from the desert with a specific mindset in the setting), Initiate (as in the Aes Sedai, specific spellcasters from the setting), and the Wilder (untrained user of the One Power, a specific type of magic user from the setting).
I chose an Armsman (basically a Fighter). It was all bonus feats. I wanted to be a soldier. I wanted something straightforward, and I got all the hooks I needed from the game prompts ("where did you get your training?" "where did you get your equipment?" "how did you end up where you are?").
When I made classes for my RPG, I made some very specific classes: Blacksoul, Bloodletter, Hand of Dawn, Magician of Nyt, Order of the Obsidian Flame, Scarred Man. I also have some very open-ended classes (Berserker, Factotum, Ranger, Warrior).
In my experience, a good mix of both is necessary if you're trying to cover a lot of character concepts while also strengthening your setting. There are standard guards (Warriors) and Craftsmen (Factotum) and Sages (Factotum) and so on, and there are highlights specific to your setting (Blacksoul, Bloodletter, Hand of Dawn, Magician of Nyt, Order of the Obsidian Flame, Scarred Man).
I think the real problem can come from the mundane classes feeling "generic" in comparison to the supernatural ones. To a degree, though, that's very understandable. We can basically have ideas of "generic" rangers or warriors or sages or craftsmen, but magic doesn't really have a "generic" default.
But, "Thief of the Red Hand" is a meaty hook, all contextual and rich in detail, with associated iconography and Proper Nouns. So is "Alteric Town Guard" and "Thaumaturgy Professor of the Arcane Academy."
I don't think I'd mind any of those, as long as there were a couple conditions that were met:
(1) There was explicit buy-in for this campaign that we were to make characters with these specific backgrounds. This isn't any different than "make sure your characters have a reason to be together" or "no humans in this campaign" or the like.
(2) The game system allowed for more than this; having a generic thief is more desirable for me than only a "Thief of the Red Hand" is.
I can totally buy into a campaign with a "Thief of the Red Hand" and "Alteric Town Guard" as classes. I can't buy into that being all there is for me to play, though.
And, in a class-based game, I'm not really excited about making 5-15 classes every campaign, especially when NPCs follow different rules.
And when all of those fit within a flexible framework that lets you change pretty much any part of those for something else, you still capture the flexibility that old hats value, better than the class structure in D&D has ever really done, even at its most open-ended so far.
This is a situation where the middle ground, I think, doesn't really satisfy either party, but when you go to both extremes simultaneously, there's a good harmony.
I think, honestly, that a mix of very setting-specific stuff and very generic stuff is better; I'd much rather have a Druid and Bard mixed in with the Fighter than your Thief of the Red Hand and Alteric Town Guard and nothing generic for me to use. At least, I have no interest in your method in the long term, especially if it requires a lot of work.
But, that's just me. Curious if you can show me how you think it'd be easy. Genuinely curious.