This is a thing that would be cool, but as some people have suggested requires a bunch of effort to work well.
Mr.Bando is on the right track for how I'd do this. Recording that data isn't hard (and is useful enough for debugging that I already have a version of it), but replaying it in a coherent fashion within the game client is a bit trickier.
Though, due to the way we handle visibility, this would mean that replays of the same match will be different for different players (you receive less frequent updates about e.g. player positions on distant other ships, and may not receive information at all if said ship is far enough away or inside cloud cover...)
In short, yes, this is a thing I think about doing.