Just because you can justify the next climb on the same basis, that doesn't mean you will. You could decide that you've already tested the odds one too many times.
Do you really think this slippery slope argument is a fallacy? FWIW, wikipedia acknowledges slippery slope can be a legit argument when the slope, and it's chain of consequences, are actually real. https://en.m.wikipedia.org/wiki/Slippery_slope . Indeed, this is the very basis of mathematical induction.
> The fallacious sense of "slippery slope" is often used synonymously with continuum fallacy, in that it ignores the possibility of middle ground and assumes a discrete transition from category A to category B. In this sense, it constitutes an informal fallacy.
"If you take N steps, you will take N+1 steps" is a fallacy whenever it's possible that you won't take N+1 steps.
"Not A -> Not B" is different logic than "A -> B". A is necessary but not sufficient for B.
Of course if you add in "you could decide that you've already tested the odds one too many times" then it's a fallacy to invoke slippery slope because an off-ramp is explicitly specified. In this case slippery slope was mentioned only because N was dismissed as irrelevant.