I don't think this is needed. The high school student fares don't need this, at least. My cousin pays the student fare on the TTC even though his Presto card was only set up for student fares with YRT.
That is correct--Presto concession fares are, generally, universal. To be fair, this is a common misconception, even @ttchelps on twitter incorrectly tells customers they have to come get it set exclusively at davisville (wrong) for TTC in particular despite already having it set for another agency (wrong).
Child, Student, Post-Secondary Student, Adult, and Senior are universal. If you get them set on one agency, they're set for all.
What happens at time of tap is that part that's up to the agency, but that has nothing to do with where you set the classification and nothing to do with anything the passenger does. For instance, a child pays a discounted fare on most agencies, but is free on TTC. Or, I used to have a post-secondary fare on my card with GO Transit; it would make the concession sound and light up yellow instead of green when I tapped it on TTC readers, despite the TTC having no post-secondary fare for single rides on Presto--I would always be charged the $2.90 adult fare, due to that, but my LFLRV transfers would be printed with 'PS1' which is the post secondary fare code...I always hoped that wouldn't cause trouble if I got fare inspected, luckily it never came up on the TTC. Similarly, before GO/UPX fare integration/when it was $19, the UPX ticket checkers would come and tap my card on their machine to check my fare, and I glanced at the machine ones and saw a screen saying 'PS1, verify passenger identification/fare eligibility' however they just clicked 'OK' on the warning immediately, since UPX did not have a post-secondary fare at the time and my card had been billed the adult fare.
But yes, the actual setting of the fare at a customer service outlet is universal for all currently existing categories no matter where you set it. Similarly to post-secondary defaulting to adult when not available on an agency like YRT or TTC, I presume 'discounted adult' set by TTC will default to adult on other agencies...presumably any such non-matching fare code would always default to adult, and presumably transit agencies will be able to set a fare code which is exclusively for their use, e.g. the TTC will likely have different metrics for the low-income fare category than other agencies should they choose to follow suit, so I'd imagine that the discounted adult code would be one that would need to be set individually. None of the current ones need to, though.