I think having the Summoners' Rift as an active thing in the lore is just bad idea at it's core. It restricts what the writers can do, creates a vacuum around it where everything else in the lore must bend to it's all powerful will (people don't like Targon sometimes for this reason) and it's just contrived way for champs in different regions to interact instead of letting it happen naturally.
Lately though I've been warming up to the idea of Riot preserving it in some fashion after speaking to people on the Boards who are longtime mainstays and had the Rift as their introduction to League of Legends lore. For their sake Riot can make The Summoners' Rift something that was canon and had existed, but is now dust and forgotten in the wake of catastrophes like Mordekaisers' Reign, The Ruination and the Rune Wars.
The Summoners' Rift can be canon, but just not in its' current condition. It has to be nerfed.
1.) Like maybe in that era between the Darkin obliterating all of Valoran and Mordekaisers' reign for aspan of about 200 years the Summoners' Rift was active and helped the rebuilding nations and tribes restructure themselves because all they knew was war. In the wake of the Darkin, people had lived full on generations just fighting under the threat of death for these corrupted god-warriors, so even after the Darkin were destroyed the people knew nothing but violence. The Summoners fill this rift of power left by the Darkin and calm the situation between warlords and feuding tribes down and establishes the Rift as blood sport to settle disputes without resorting to all-out war.
2.) The Summoners can't be all powerful juggernauts in this future iteration, instead they must use political intrigue to try and encourage nations to coexist, but much like modern nations some people don't wanna play ball (Think of Mordekaisers' Proto-Noxian Empire as North Korea in this metaphor). In the old lore the Summoners kept even mighty empires of Noxus around because they were capable of devastating feats of magical annihilation on par with the Runes capability. This can't be the case because it downplays the power of the Runes (which is what the Summoners exist to hype up in the first place) and like I said it creates a gravity well effect where the lore slowly starts to be built around this concept because of how powerful it is and the stakes it presents. The Summoners should be strong no doubt, but not strong enough to challenge juggernauts like modern day Noxus... or Mordekaiser who in this universe would probably be the cause of their downfall.
3.) Shift the Summoners' power away from them and INTO the Rift. The Rift is still around and it presents a story hook for nation to compete with each other for today. It gives it a relative reason to have existed and matters in the current Runeterra and makes this effort to bring them back about more than appeasing the nostalgia of long time fans. Maybe the Rift is home to some magical anomaly that is building up power and people could want to use that to their advantage. Now we as readers know there is this place somewhere between Demacia, Freljord and Noxus that hasn't been rediscovered, but should it be... it could spell disaster for Valoran. Also yeah it's a Valoran thing. The League of Legends and the Summoners' never had influence over Shurima, Blue Flame Isles or Ionia because that just isn't realistic for this new scope of the organization...
If Riot wanted to do even more with the Rift they could have the story be about certain like minded champions restarting the League of Legends. Champs that don't see borders and recognize that different people must learn to live together to not repeat the sins of our forefathers and plunge the world into war like it has been so many times before. 
maybe...
come to mind as people who would see this way. That wouldn't be necessary though as the point of this isn't to make the Rift the point of the story any more, but just to find a way for it to exist in the current lore.
is actually like an Oracle of sorts and that summoner's rift is a thing still, it's just not a political thing anymore, it's simply where all powerful summoners conjure likenesses of champions from Runeterra to fight each other and Sona being able to commune with summoner's which is how the Sona player can hear Sona's "Voice"
I get that the institute of war was scrapped because "why would someone like 
heed the call of a summoner for politics" however I feel that if Sona lost her "voice" it would suck, and there would be outrage.
lost all his dialogue, especially since Sona doesn't have much dialogue to begin with, but imagine if Sona was actually magically attuned to all the other versions of Sona and thus knew a lot about future potential realities and thats why 
