That's the one that I think is the gold standard for when the artifice doesn't work.
Depends on the artist. The performative aspect of a character as it relates to an album cycle is, I think, more of a commercial decision than anything. It signals that the artist is doing something, that an experiment is happening, that they deserve your attention. It rationalizes developing new merch and provides a central thesis around which you can develop promotional materials, album art, interviews, live show visuals etc.
There are musicians whose whole thing is that they are authentically themselves. Nick Cave is the example at the top of mind because one of his most recent Red Hand Files was explicitly about chasing authenticity. Cave isn't a "rock star" in the sense that he's headlining arenas, but I think you'd be hard pressed to think of many artists who have been around as long, lived as hard, been as prolific & acclaimed, etc. Putting on a character might -- MIGHT -- make him more 'relevant,' but what he's done instead has preserved his integrity & reputation as a capital-A Artist.
But as you guys have touched on, there's multiple flavors of this. There's the album-based character cycle, where it's like an interchangeable outfit that you can put on and take off. There's the artist that is inseparable from a very specific character (DOOM is a great example, but also KISS, GWAR, Weird Al, etc.). There's the artist whose private persona and stage persona are publicly acknowledged to be very different (see "Sasha Fierce"). And then there are artists who demonstrate an honest and sincere evolution of their artistry over time. For this final category I'm thinking more of the Nick Cave types, but it's not exactly uncommon. Ideally you want all artists to evolve over time and add layers and dimension to their work, to be in conversation with their lives and the world around them. But you also want to be more substantial in nature than the cliche of a band whose second album budget is a blank check to write the biggest possible anthems so that their sound fills bigger and bigger venues.
To summarize, I agree that "X album's character is Y" is a crass, mostly commercial, choice, and it's different from maintaining an artistic/stage persona that is not the same as who the artist is privately. You want artists to demonstrate growth, but in a world where everyone is vying for attention and nuance is hard to come by, it's easy to understand why the album cycle shtick is a popular formula.