That's true, the stake in this proposed system is equivalent to a half wager (in terms of risk analysis). However, risk analysis isn't the be all end all.Good. We are agreed then that in vanilla-PHB, failing an ability check comes with a consequence. That's why we called for a check in the first place.
My word, but this is splitting hairs. Yes, if your rope could be consumed or will become unavailable for several sessions, then it can become a cost as well as a requirement.
Solid criticism. What that points to is that it is correct to have drawbacks on odds for both failure and success. Else all that happens is we dilute the cost of failure (roughly halving the wager).
Something is at stake. I mean, one does not say in gamlbing that nothing is at stake because I might not lose. Roughly, the method can be said to halve the wager. Where loss on a fail was guaranteed, now it is guaranteed half the time. On the other hand, sometimes I now pay a price with success. There is no abandoning of stakes, only a rearrangement of how they fall.
I understand that coming to this from vanilla-PHB, one feels like "success with a cost" isn't "failing forward" even though the outcomes are isomorphic. And that we're used to success being unadorned succes - I got what I wanted, no drawbacks - and failure to always have a drawback. In intent, that is what the DMG options do. "Fail" by 5 or less? No drawback. "Fail" by 2 or less? Actually that's a success, but here's a drawback. The list of outcomes implementing the DMG options puts on offer, is the same as the list of outcomes with this method. Even while the methods and probabilities differ.
I don't dismiss the importance of semantics, but in designing mechanics I am thinking about what the mechanic genuinely does. Success at a cost == success at a cost even if in the past we might have called that a "failure" that turns into a success with a cost.
If you look at what the mechanic genuinely does, you see that on a failed even roll it does nothing.
It would be as if you and I were playing a hand of poker. You win the hand, but then we have to flip a coin to see whether you actually get to keep the pot, or whether we play a second hand to decide the outcome. If you keep winning and the coin flip keeps saying we play another hand, we might have to play a third, fourth, fifth, or even more hands. That's not fun or interesting. It's just stalling out the game and rendering the previous hands meaningless.
I could maybe see this having an application in very specific scenarios. You're already climbing and I want you to have both a chance of failing to make progress (because there are hobgoblin archers aiming at you) and a chance of falling. That said, I would either use the total result of the climb check to determine that, or ask for a second climb check if the first failed. The benefit of both of these is that, rather than being up to a coin toss, they both take into account the character's actual skill at climbing when determining whether they stall out or fall on a failed check.