This isn't true.
In AD&D, to hit rolls are resolved on d20. But the chance of a 1st level fighter defeating a storm giant in hand-to-hand combat are below 5%.
Apples and oranges.
The chance of a 1st-level fighter
defeating a storm giant is extremely close to zero. But, the chance of that 1st level fighter
hitting that giant on any one particular roll, while not great, are far enough away from zero to make the roll worthwhile.
In AD&D, a 1st level human thief has an 85% chance to climb walls. This could be represented on a d20.
It could; 85% is very neatly represented by 17 or less on a d20.
But what if the chance is 98%? That's not representable on a d20 yet is still most certainly not a guaranteed success...says he, who has had characters fail resurrection on odds like this more times than I care to think of.
According to the DMG (p 19), a check must be made very round - which means every 9' climbing a typical slightly slippery dungeon wall. The slight slipperiness also doubles the chance of slipping and falling, ie to 30%. If the wall the thief is trying to climb is more than 72 feet high, the chance of success is less than 5% - eg a little over 4% if the wall is no more than 81 feet high.
I long ago streamlined this by concatenating it all into a roll or two: the first to succeed against the rough overall odds of success (e.g. let's say 4% for the 80' slippery wall in your example), and a second to gauge roughly how far you'd got before failure if the first roll does not show success. The second roll is weighted toward failing early; as most often if you're gonna blow it, or realize you're not gonna make it, it'll happen shortly after leaving the ground.
That's another peculiarity of AD&D that reduces its flexibility - some actions are resolved with a single die roll (eg opening a lock, searching for a secret door), others are resolved with multiple rolls (eg combat, climbing certain distances), others allow retries (eg forcing open ordinary doors; listening at doors) - with no apparent rhyme or reason.
To me, forcing open a door* comes under the same category as picking a lock; your roll represents your best shot at it and you don't get another until-unless something materially changes. In the door example this material change might be as simple as getting a second party member to help you.
* - actually, this is much more akin to bend bars-lift gates, which are specifically called out by example as only getting one roll (or only one roll for each if trying to get through a barred gate) without material change.
As for listening at a door, the material change here that allows another attempt is simply the passage of time; the PCs have no way of knowing whether something has materially changed beyond the door that might produce a different result than before.