It sure would be handy not to have to let the replay viewer run for 55 minutes recording the replay as it replays in order to save that epic game in a format that doesn't become useless in <2 weeks.
Solution 1: Riot implements a system where the game checks what version the replay is, then downloads an appropriate old client version and uses that to play it.
Would also cost Riot a bit as they would have to host old client versions and send them out periodically to players trying to watch old replays.
They could mitigate the impact on their servers by having the patcher keep old client versions for a few patch cycles, but this would have the downside of bloating League's filesize.
Solution 2: A button that says "record remainder of the match". Would still require tying up the user's computer for the length of the match but...
Riot could mitigate this by having the replay viewer play at the maximum speed the user's computer can handle without resulting in a framerate drop, then slowing the video back down after recording has finished. However, this would only be helpful to users whose computer can render League at 2x speed and 2x framerate or better.
Solution 1 is good for users with plenty of harddrive space.
Solution 2 is good for users with powerful computers that can run League at high framerates.