I think it would be helpful to include a sidebar with a suggestion along the following lines, possibly in the skills section or the running the game section.
If your vision of your character's history would conflict with the applications of the rules in some way (such as an character with a trained or better proficiency rank in athletics that has lived their whole life in the desert and never learned to swim), you can choose to voluntarily reduce your proficiency rank for a subsection of a skill or other rules element below its usual rank. The default assumption for this reduction (as with the example above) is to treat your proficiency as untrained in the area in which your character is deficient. This means that you do not qualify for any feats or options that depend on your proficiency if they would relate to that aspect of the rules. (As with the example above, a character with Legendary proficiency in Athletics that has chosen to be unable to swim would not qualify to take the Legendary Swimmer skill feat.)
It's important to confer with your GM and your play group before taking a voluntary penalty like this, to make sure that doing do will not be disruptive to the group or the story in which your character exists.
If, after taking such a voluntary penalty, the story changes in such a way that causes your character to overcome, or seek to overcome, this weakness, you can use downtime for retraining as though you were retraining a proficiency increase. With each use of downtime in this way, increase your proficiency rank in the area you took the voluntary penalty once, to a maximum of your overall proficiency in the area. Once your proficiency in the area in which you took a voluntary penalty matches your overall proficiency, you no longer need to count its proficiency separately. (As with the example, a character that is a Master of Athletics, but is unable to swim, could use retraining to improve from Untrained proficiency in swimming to Trained proficiency, and could do so again to reach Expert, and then again to reach Master, but could not continue retraining to achieve Legendary proficiency since they lack Legendary proficiency in Athletics.)
I see the argument pop up every so often that the +1/level skills system makes no sense, and sometimes the argument is based on the way that certain areas of competence are lumped in together with the way that PF2 is streamlined. Having something like this codified in the rulebook this allows someone for who this is a conceptual problem to have a well-defined path for assuaging their cognitive dissonance, while also including a helpful reminder that you should make sure you aren't being disruptive.
Also, by not including any mechanical benefits (just psychological ones), and by giving guidance for how long it should take if you later reverse your decision, you don't accidentally provide any incentives for whole swathes of the player base taking, presumably roleplay-based, disadvantages for personal power - but only to fulfill their character concept.
It is a well written post. But I don't actually think that the problem actually needs a sidebar to fix it. Anyone who is actually building their character for role playing focus would already know this.
I think that people just use this logic to throw mud at the skill system.
I don't think we need to actually mechanically reduce proficiency, I think it's fine for a player to just declare "My character would have no idea how to do that" and then choose not to roll even though you could.
Like in PF1, I voluntarily choose not to roll perception or some other skill check I could attempt untrained but would be something my character would actually succeed at all the time; so I'm not totally sure how "despite my athletics modifier, my character does not know how to swim" is different.