Eh, I'm staring to see where I have issues with this approach as well... mainly with causality and narrative control.
So because I didn't succeed at climbing... the DM now gets to create consequences which, while they may follow from the fiction can be unrelated to the fact that I failed at a climbing check... Looking at this from the perspective of a player... I want my consequences to flow organically from what I did or did not accomplish with my rolls. Why? Because that's the character I built... either I'm a great climber and this is one of those rare mishaps everyone suffers at some point... or I'm not that good at climbing and I knew that when I tried this, either way my character messed up climbing. What my character isn't known for are his fumbling fingers, so why am I suddenly a butterfingers or so incompetent I didn't tie down my divining rod? This approach also makes it difficult for consistency in knowing (at least in general) what the results of failing at something will be.
As a player I'd also wonder just how far these consequences can go, which was part of my objection to the earlier example where failing to find a trap while searching for it suddenly put me in the position of having activated the trap itself... I'm loosing agency here both in my character's actions and in the narrative of my character itself.
As a DM... for me it does feel kinda railroady since I am inventing what I want to happen on the fly... How do I guarantee that I not push towards the outcome I want and/or what I find fun, interesting, etc? The other side of that question being, how do I know what I find interesting or entertaining for other people's characters is what they also find entertaining or enjoyable at that moment? In the climbing example, what if a player would have preferred falling into the crevice below and taking his chances with whatever denizen was down there... if he survived? It also seems like in failing forward, regardless of the scenery of the path... the path still leads to the top of the mountain, which also feels kind of railroady... I won't go so far as to say it leads to a railroad... but I will say I can see where one can get that impression from.
Depends on the style used. I am not a fan of utilising consequence that does not follow from the failure since that can muddy in-character thought processes in ways I find disconcerting as a player. More typically in my case, the failure will in addition trigger an event / effect in the environment that is already plausibly present, but presently undetected or apparently inconsequential. If there is an option to introduce a new stake (such as dropping a valuable item), I'll present that to the table as a choice in advance --> the player fails a climb check* sufficiently badly that a fall is a normal consequence and the player is presented with the option to accept the fall or drop the item as he desperately grabs for holds.
Can the technique be used to railroad? Sure. Any technique that relies on GM force can be used to railroad. The GM needs to guard against (or at least be honest with himself and the table) as he would with any other technique.
* this is a poor example for the way I typically use fail-forward which is more about when the players have painted themselves into a corner and the situation is threatening to enter stasis and/or the table is furiously pursuing a self-created red herring out to sea.