When accounting for human psychology it does have validity: doing an enjoyable activity "one more time" has a risk of a habit forming, which has a non-zero probability. It is indeed possible.
The argument can certainly be used in a fallacious manner (e.g. by greatly exaggerating the probability of the further steps, saying they are inevitable if the first step is taken, etc.). It's logically valid to say that the first step enables subsequent steps to be taken.
Edit: I'd say that the slippery slope is perfectly valid rule of thumb in a lot of 'adversarial' situations. Once one side makes an error or fails somehow, the balance between the two sides can be disrupted leading to one 'side' gaining momentum. Just as between people, a similar 'adversarial' process can occur within the minds of individuals: between two ideas or patterns of thought/behaviour, one idea can gain momentum after a decision has been reached. Precedence is a strong force.
Slippery slope arguments aren't inherently fallacious. If you can justify one more climb on the grounds that probability of injury or death is very low then you will be able to justify every subsequent climb on the same basis.
Slippery slope arguments are inherently fallacies. They don't prove that something will happen.
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.
Don't get on that greased sliding board that ends at the top of a cliff. Once you start sliding, it will be hard to stop because of the grease, and then once you slide off then end you will fall and die.
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.
"You could decide that you've already tested the odds one too many times" was the original point. Someone responded that the N previous times don't matter and N + 1 has barely any risk. Another poster countered that that argument as stated applies not just for N + 1 but for (N + 1) + 1 etc and therefore the slippery slope principle applies.
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.
Maybe fallacies could be renamed "logical hazards" or something like that. Arguments that are at high risk of being false and require extra care, but not automatically false.
It's a convincing fallacy because sometimes you do take N+1 steps. But just like in the article, heuristics aren't always right.