For skill panel suggestions, it's important to be aware that both the full and compact panels exist, just to clarify what is actually being suggested.
If I have it right, this suggestion would apply to the full panel only -- users of the compact panel have already chosen to do without "load replay" and "clear physics" buttons, so it doesn't make sense to push a "save replay" button on them.
Adding an extra button, while keeping the panel the same size, would obviously require shrinking the minimap. It's already pretty small, and most levels are wider than they are tall, so I don't think that's a good idea unless there's a really strong reason for it. (It's true that the minimap doesn't cope well with tall levels, but that's a separate problem, and I'm not sure there is any good solution.)
A "save replay" button does make obvious sense -- the only thing against it is that many users have automatic replay saving on (and I am pretty sure this is on by default), so perhaps there is less need for it. But as I said in the "show skills used" topic (and namida has agreed), this is far too niche a feature to justify a button. The save-'em-up contests are a lot of fun, but other than that, have you ever needed to see how many of a skill you've used? I suppose it's also useful for SYCLW challenges, but those are already tracked by the engine.