Li Shenron
Legend
Like shooting a free throw. You can fail 10 times in a row and do the exact same thing every time, then make it the 11th time. Even the pros, who use the exact same technique and process, never succeed every time. They certainly don't learn what they did wrong when they missed, they do the exact same thing on the next attempt. And by missing, it certainly doesn't mean they realize they can't succeed. That's nonsense. They try again, using the same process.
I was totally expecting EXACTLY the example of a free throw in basketball. It is the worst possible example to mess up the understanding of how the rules of checks in D&D are conceived across editions.
Truth is, the basketball free throws are not an example of trying the same thing over and over until you succeed (once) and then you're done. What defines "success" in keep throwing infinitely until you score? Eventually you score, there is no chance of failure. If that's the case with a skill in D&D, there is NO point in the DM asking the player to roll in the first place. (Note that instead, throwing the ball in the context of a match is akin to rolling attacks, with each throw/attack being a challenge of its own with a separate outcome)
At most, in some cases it might be interesting to consider, if someone has a small chance of success but can keep trying indefinitely, how long it takes before succeeding. So instead of re-rolling the DM could just roll once for the time required. Or if multiple successes build up better results (as in crafting rules typically), roll once to quantify such results. In all cases, ONE ROLL is all you ever need, except perhaps a special occasion when the outcome has more than one dimension.
But if the outcome has one dimension only, complicating the rule only gives the illusion of improvement, and at worst it can wreck probabilities to the point of becoming moot to roll at all.