Well yes. Assume an average adult in good health with no specialised training (Str 10) with a movement of 30'.
He has a 25 percent chance of falling on a DC 10 every 15' he travels and a 50/50 chance of getting a further 15' up.
To climb 50' he needs to make 4 such checks without failing 1 or he falls. On average it takes him 8 checks to get those 4 successes and he would fall off rhe wall more often than not in getting those 4 successes.
Compound checks are a bad idea and should be avoided where possible.
A rough hewn wall like a climbing wall at a gym shouldn't be more than DC5. With ropes it shouldnt even be a check af all. An adult himan in good health (Str 10) can climb such a wall every time he tries.
Ok, so we'll go with your +0... Yes, 4 checks.
Rolls 10 or higher (DC 10) and climbs 15 feet. Rolls 5-9 and doesn't make any progress. Rolls 1-4 (only 20%) and he
might fall. He then rolls a DC 10 DEX save (let's assume +0 again) and only falls on a 9 or lower (45%). So, the chance of him failing a check
and a save is only 9%.
FWIW, the chance of him making 4 checks
in a row is 0.55^4 which is 9.15%.
That alone is higher than the 6% you claimed before. And that is making 4 checks in a row. He can easily make a couple, fail one without falling, and then continue the climb.
Overall, a person with a +0 modifier has about a 55% chance of falling at some point during this climb, or they have roughly a 45% chance of making it to the top. Those who make the climb will average about 6-7 checks.
(Roughly 17% fall before making it to 15', roughly 17% fall between 15-29', roughly 11% fall between 30-44', and roughly 10% fall while making the last 5' from 45-49'.)
For someone with no STR mod and no proficiency in Athletics, 45% for a 50' climb seems really good to me (in fact, it is probably
too high).
For a +4 modifier (maybe a little STR and/or proficiency) and the chance of making this climb leaps to 88%, without ropes, a climber's kit, or anything.
You have to realize we aren't talking about a rock wall at a gym (
which people do fall from, even if they know what they're doing... hence the safety ropes, etc.), we are talking about a wall in a natural setting where a hold might not support your weight, a root could pull out, etc.
Compound checks are a bad idea and should be avoided where possible.
As your opinion that is fine. A lot of games use compound checks and IMO they add to the suspense of the situation. So, when warranted I have no issue with them. Since you do, as I said before, I guess it is simply a good thing you don't play at our table. No issue with that, by the way, to each their own.