I think the reason for not having a replay system, is due to the "fog of war" in the anti-cheat.
because it doesn't render all the players at all times to prevent wallhacks, it may be impossible for the client to generate the replay file.
this means RIOT servers have to generate the replay and send it to the clients, for every single game played. this is obviously not easy, since RIOT uses their own servers instead of AWS / GCP.
EDIT: Since my intentions have been misinterpreted, I want to clarify that this is not to say that there shouldn't be a replay system, but to highlight potential reasons why it may be taking longer than expected. These problems may require infrastructural changes, which in the current state of the world, could be slower than usual.