This is literally the point of the basketball example. It is meant to be an example of a situation where there is no power my in rolling. There is a chance of success, a chance of failure, and no cost or consequence for failure, therefore you eventually succeed and no roll is necessary to determine that.
That really gets to the nature of the game, and what you hope to get out of it. For a lot of DMs, the point of the roll is to figure out what happens, so they know how to narrate it; different rolls beget different narratives, which is important when you want to know how it goes. "You throw the ball into the basket," is a different narrative than "You try to throw the ball into the basket, and you spend some time chasing the ball around, but you eventually succeed after an embarrassing number of attempts." Especially when you're practicing free throws, that's a big difference.
If the character has some further goal, like they need to knock a bird nest out of a tree so that they can get a gem from inside, then it's probably safe to ignore the roll and just move on with the narrative. "It might take a few tries, but you'll eventually succeed, so you get the gem."
Interesting. See, I want the player to know that if they do X and I ask for a check, that X has a chance of success and a chance of failure. And I want them to have confidence in the consistency of the world, which means unless something has changed since they last did X, doing X again must still have a chance of success and a chance of failure.
There's a fundamental difference between what rolls represent in different game systems. What you describe is one approach, where a 65% chance means that all of the existing variables yield a 65% chance of success, and the die roll represents minor variations like wind and focus and sweat dripping down your hands; and no matter how many times you repeat the test, those minor variations will always be uncertain.
The other approach is that the die roll represents persistent factors. If you have a 65% chance, then it means there's a 65% chance that the unknown variables will allow you to succeed; but once you roll, and it's revealed whether those factors are in your favor, then those factors remain relatively constant. You either know how to pick this lock, or you don't, and we don't know which is the case, because we aren't manually tracking all of the relevant factors; but once you roll, and we know for a fact that you can't do it, then those unknown factors are no longer unknown.
Unfortunately, which model a game is using, is rarely made clear when reading the book. It's a relatively safe bet that the first model applies to attack rolls, saving throws, and free throws. The second model may apply to picking locks, breaking manacles, or knowing the capital of Assyria; or it may not, depending on the DM.
TLDR - I think I'm agreeing with you, but I've spent too long working on this post to justify canceling it at this point.