In light of admissions by other QBs that they DID tamper with the footballs after the officials had inspected and approved them, the NFL probably should have been doing this before.
Yes, each team provides their footballs for the game, but Dean Blandino and other NFL personnel have claimed or stated that EVERY game ball is tested. Moreover, the NFL has admitted or claimed that each and every game ball was allegedly tested and found to be legal before the AFCCG.
I've never claimed or even suggested that the Pats' miscalculated the psi. However, the NFL's statements disprove your allegation that "not ALL balls are individually tested (as they aren't required to be)" because the NFL has asserted that ALL game balls were tested and are required to be tested. Therefore, if a football team provided footballs to the officials that were either under-inflated or overinflated and the officials failed to properly test the footballs before approving the balls for the game, then in that situation I suspect you would be in the extreme minority to think that was cheating. Almost every player or former player I have heard speak on the issue has essentially said it is only cheating if the team tampers with the footballs AFTER they have been approved by the officials.
I haven't heard anyone, except you now, allege or claim that the Pats deflated the footballs on the sidelines during the game while a different game balls was in play.
See above for my response to your first point.