If each reversible step was clearly marked as such, I don't see a problem with starting at the goal and then working towards a trivially true statement. Usually the problem is that the steps are written down without explaining how they are supposed to relate to each other, so you are left to guess based on the order they are written down.
Across two math departments that I have taken courses with, this was handled by having an official document that explained how to write proofs ("Read this if you want to pass the homework requirement."), then mercilessly marking down any missing details (e.g. whether two statements are equivalent).
This was probably quite a shock for many who hadn't needed this kind of rigor before, but they did learn pretty quickly to state their proof attempts according to the guidelines. (There were still mistakes, of course, but at least they were less ambiguous.)
A proof is more than just a collection of true statements: it is a means of communication. And in a classroom it is also a demonstration of knowledge. Even if every step is technically correct, the presentation may not be sufficient for full marks. Depending on the class, we may or may not have high expectations for a proof. Also I don't believe the students ever once made this setup but remarked that the steps were reversible, but I would give that full points with a little note that it could be better organized.
I've never encountered a formal "do these steps to make a proof" document. I'd have to see it, but it could be a good idea.
Across two math departments that I have taken courses with, this was handled by having an official document that explained how to write proofs ("Read this if you want to pass the homework requirement."), then mercilessly marking down any missing details (e.g. whether two statements are equivalent).
This was probably quite a shock for many who hadn't needed this kind of rigor before, but they did learn pretty quickly to state their proof attempts according to the guidelines. (There were still mistakes, of course, but at least they were less ambiguous.)