I'd love this, however they were changed and riot can't go adding dual options for a champion- they could make it so it was clearly marked you were playing an old school version of a champion but... Just over complicates everything.
That being said, I would think they could easily implement this in a game mode- temporary or permanent if it was popular enough. There is a large enough pool of reworked champions to pick from; Completely reworked champions (Shen, Warwick, Rengar, Ryze [all variations] Poppy, Mordekaiser, Yorick, Sion, Fiora, Gangplank, Taric, Skarner, Xerath, Heimerdinger, Sivir, Olaf, Soraka, any others I missed), and significant-half-kit overhauls like the Class updates (Assasin, Mage, Marksman, the semi group support update from way way back). I hesitate to include any champion who had only one or two abilities completely changed, which may eliminate some of the champs from the group Class updates. If Riot felt a larger pool was needed, they could certainly add any champion with a large visual rework or small ability changes (like lee sin with a lot of his abilities utility passives restored.
To add to the nostalgia and overall content, it only makes sense to add in discontinued items like Heart of Gold, Philosophers Stone, Wriggles Lantern/Feral Flare, Deathfire Grasp, Force of Nature, Shurelyas Reverie, Twin shadows, Spirit jungle items, Sword of the Occult, and Will of the Ancients. There are many others, but I think I named all those with nostalgic and historical significance (used to be well known/important/broken/overpowered).
There's zero expectation (or want) for Riot to go through and balance champion/item stats; I.e. Just plop the champions and items in with the last numbers they had before rework/removal. I think his would create a game mode that many veteran players would love for the nostalgia, and an opportunity for newer players to experience playing old versions of champions and using items they've only been able to see in videos and hear first hand from players who played then. Imagine one jungled with feral flare and the opposing with wriggles lantern, or Spirit of the ancient golem; or original Ryze facing season 4 Ryze; getting able to play an old version of your main now that you've only seen in videos or taking a trip down memory lane.
I would love to have a chance to play old Shen (and all of those champions I listed) again. I completely understand and support gameplay updates to keep champions viable and he game as a whole in a healthy state as it is now a huge spectator sport, but a harmless game mode like this would be absolutely amazing imo. As fun as the assasin update is, this would have a lot more significance for veteran and new players alike in regards to playing old content that has no influence on the current state of the game, and the added bonus of having fun with different eras of champions and items existing together in the same game for the first time.
