@BryonD
At the end of the day we are all sharing our subjective aesthetic judgments. I consider games works of art meant for popular consumption. Like any other art form there is no objective measure of what a role playing game is or should be. The diversity of play that exists from Pathfinder First Edition to Monsterhearts back to Fifth Edition suggests to me there are many functional ways to make a role playing game.
My personal aesthetic judgement based on playing game and reading through the material is that Pathfinder Second Edition is very concerned with helping its players build a narrative through play. I have never felt more like my character in an iteration of Dungeons and Dragons. I rank it up there with Masks, Monsterhearts, and Exalted Third Edition when it comes to correspondence between narrative and game play. When I play my Barbarian I feel impulsive, arrogant, and angry. The mechanics of the game help me feel what my character is feeling. That includes the level based scaling.
It absolutely helps the players build a narrative, although probably not of the type you personally value. That's fine. Different game provide different sorts of narrative experiences.
I suspect the disconnect here is that you do not consider character class and character level to be things that have narrative significance. My personal aesthetic judgement is that for a game to feel like part of the Dungeons and Dragons tradition there needs to be thematic significance to character level, class, and race or ancestry. Each should tell us something meaningful about who the character is. When I say I am playing 5th level Dwarven Fighter there should be a cultural resonance to that. That's not all of who he is, but those choices should tell us something.
For me there has always been something ancient and primal about character level since I started playing Dungeons and Dragons. The clarion call of name level has always been a large part of the appeal to me. Level in Dungeons and Dragons has always been about more than an abstract measure of power. It has also always been an indicator of narrative significance. Over the course of your adventures you do not just become more skilled. Your narrative importance increases as well. Even though there are not mechanics for it yet Pathfinder Second Edition explicitly calls out fighters establishing keeps, rogues starting a thieve's guild, wizards starting a school, and clerics building a temple in the roleplaying advice on the first page of each class.
This is what I was trying to get at in the other thread. The mechanics make level important because it is intended to have narrative significance. It does not just help determine combat stats and skills. It also affects things like Recall Knowledge checks to know things about the person, place, or thing. It affects how difficult it is to craft an item. It's harder to make an impression on a higher level creature because they have more narrative significance. The game views the entire world through the prism of level. A religious text might have a level that portrays its narrative significance and will determine how hard it is to translate or know about with obvious adjustments for fictional positioning. A task might have level which determines how hard it is to convince someone to do.
When something designed for the game and they assign it a level they are making a narrative choice as well as a mechanical choice. Goblin Warriors are level -1 not because they decided there was a need for a level -1 creature, but because he is less significant and powerful than a starting player character. Within the scope of the story he has less significance. This is not a game with a set adventuring day or expectation of encounter difficulty. They provide tools so the GM will know how difficult an encounter may be, but no guidance on what adventures should look like. The examples in the book include tasks well above the characters' level.
The mechanics you bemoan are intended to bring this level as a measure of narrative significance to life in the minds of players. They want you to feel the significance that comes with being higher level. They want you to feel what it's like to face the same adversaries you faced a couple levels ago in whatever context and see that you have gained power and significance. They want it to be easier to know things about them, easier to do things to them, and have it be harder for them to do things to you. They want that religious text you could not decipher to be easier to decipher.
They want you to feel more important.