Is there much benefit in memorising proofs outside of an exam setting?

I fell into the trap of memorisation. Work through the proof, understand what is being done. You will not need to memorise. You will remember key plot points simply because you've spent time on the proof and relevant definitions (learn math by doing it). You can carry on from there independently.

Also, use the whole semester to study. Don't jumpstart your engines 2 weeks before the session.

You do not study proofs because you need to memorize them, you study them because you want to understand them, and when you understand them you should be able to more or less easily reproduce them to someone, if needed.

When you understand proofs of some statement and when you also understand that statement then you can try to find some other proofs of that same statement, and, it could happen that with other proof-approach, that that statement could be generalized in a way that those proofs other than yours were not able to accomplish.

It is natural that some proofs can be called too technical, or too long, or tedious, or even ugly (did I really wrote this?) and then there exists a need to give as simple and as beautiful proof as possible of some statement and that is possible only if you know techniques and constructs that appear in rather different approaches to the same problem.

For me, the key feature of understanding proofs is the understanding of techniques that are "beyond" proof, for example, if you want to prove some fact about some class of functions you could approximate that class with some other classes that has some feature and then pass to a limit to obtain conclusion to a class that is the limit of those classes.

Here, a notion of approximation and of the limit are important, and they arise almost everywhere inside analytical studies, whether you approximate irrationals with rationals, or some enough times differentiable function with its Taylor polynomial.

When you learn laws of powers in arithmetic then you start to observe that those laws do not depend on the actual nature of the elements but just on associativity and commutativity of an operation that operates on them, but that could not be easily understood if you did not understand that on some concrete structure first.

So, if you were to ask me, more important is to understand general techniques that appear in wide variety of proofs along different branches of mathematics than just concrete proofs, but general techniques can hardly be understood if you did not first understand proofs in concrete settings.

So, if you do mathematics and like it, surely it is good to understand proofs as best as you can, to that point that you can explain them to your fellow colleagues if they stumble upon something they do not understand. The key is to co-operate and discuss those topics that you study and do.

Understanding a proof means, you need to understand the full idea as a whole, getting every line of a proof but not getting the whole picture is not actual understanding. So, if you understand the proof, no need to memorize it. It will not harm to understand proofs outside your course.