So, a new skill requires (Nature) tests, then jumps immediately to rating 2; it’s never rating 0.
Is the Advancement section suggesting that when a skill is reduced (due to sickness/injury/whatever) to zero it stays on the character sheet? Then, rather than relearning the skill from scratch, you advance it as an existing but useless skill?
If that reading is correct:
To my novice eyes it seems in a lot of ways easier to dump the skill and learn fresh. The existing skill means you’ll need to tap Nature to have a reasonable chance of success until rating 2 or more probably 3. Starting over means using ((Health or Will)/2)+1 or so dice, but doing so for free.
So assuming you tap Nature to get to rating 2, I guess it’s easier but more expensive: two successful tests, costing two Persona Points (more, if you’re not successful on the first two tests you make), rather than your Nature in tests of any outcome, for free.
Please compare this to how it would actually work in a game. I’m running my first session in a couple of weeks so this is all still coming together in my head.