Even so, regardless if they have 100% of their old versions backed up (which I still believe they do somewhere because it's code and there would be literally no reason for them to scrap it over just putting it all in a backup folder for references), it's a multi BILLION dollar company. There is very little they wouldn't be able to accomplish if they had their mind set on something, for example this game mode. It might take them some doing, sure, but it's 100% doable.
Game modes don't make money, skins do. If the decision was based on what is going to make more money for them, they wouldn't even bother making new game modes, they'd focus all their attention on new champions and new skins. You can't accurately predict how much attention it would get, there are too many variables.
That being said, I respectfully disagree with your opinion. There are many veteran players who really enjoyed the game back then, who would love being able to play in that time period again. Likewise, there are also newer players that have no idea how the game was back in the day, who would enjoy seeing what it was like back when everything was different. It's a new experience.