Its not that hard to understand why the League was not good for stories. There would be no civil war in Freljord, Azir's and Xertah's beef would be finished in a single match. The league is a superior way of dealing with conflicts, period. This was established with what occurred in both Kalamanda and Ionia. Both were spiraling towards conflict and devision, both times the League stepped in and solved the problem.
Thats bad. Good for the world stage, good for the existence of the League, but ultimately bad if you want to see Ashe and Sejuani duel in the Tundra, or would like to see Katarina cross blades with Garen in a dark alleyway in Bilgewater. If you have a problem, go to the IoW. There's no reason to inflict collateral damage.
Thats at least why I think Riot decided to start over. If the new lore will be good, hard to tell. We've had so little of the new Runeterra exposed to us. All we know about is Shurima, Noxus and maybe Freljord. What about Demacia, the Void, Ionia, etc etc etc?
We'll see. Once all of the Factions have been fleshed out... THEN we'll see if the global Runeterra has better story-telling than the JoJ lore. Of course, how long we'll have to wait for all of the Factions is another bloody question and ultimately we just need to be patient, which of course we've been for SO DARN LONG. As a person who joined LoL in 2012, I can attest to how dismal this wait has been, and I can only guess how painful it has been for others.
The argument that the IoW inhibits all conflicts is an oversimplification. The IoW did not stop the war between Noxus and Ionia, because Ionia wasn't part of the League. Then Ionia, after a whole lot of protests and Lee Sin setting himself on fire in such instance, managed to get an agreement with Noxus on settling the thing with the IoW. It's a different process from what you implied, but it's not really the point I want to make, I mention it just for the sake of it.
The point is that, as many have argued here on the boards, the IoW is not omnipotent nor omniscient and even in Kalamanda they had to sacrifice an unvaluable Nexus and risk the lives of hundreds of summoners to pull off their time-stopping stunt. If Demacia and Noxus were to go at war all over the IoW couldn't simply deal with the logistics involved in getting hundreds of Summoners all over the world to stop the war, all the while depleting their stock of ancient artifacts.
Besides, the IoW was composed of summoners, all of whom had a nationality and/or an affiliation. They were a human organization which showed its flaws: there could be corruption inside it, as the Kalamanda arc points out.
After the Kalamanda conspiracy, nations had a reason to support and trust the IoW less, thus depleting its resources.
Internal conflict could have easily started inside the IoW's factions.
The whole point is that the IoW was a constraint only as much as it was a plot device and as much as they wanted it to be. It's not hard to devise ways for the IoW to fail, causing mayhem or whatever, it just takes the effort to think about it.
Regarding champions being unable to clash in the old setting, that is not true: Malzahar and Kassadin clashed twice outside the FoJ and the second time they killed Karthus as a side-effect. They were stopped, at last, it's true, but only because the second time they fought near the IoW's facilities: if they had fought elsewhere like the first time, they could have come to a bloody end. It was the writers' will not to have neither of them dying, but they could have done it, the setting itself didn't prevent it. The only thing the setting prevented was champions killing each other at the Institute of War, but the JoJ reported widely how champions were completely free to act and be in danger outside of it.