Destroying the League could be interesting as a plot turn, if Riot really wants to explore the Leagueless version of Valoran for a while. (We might do something like that in Factions, actually.) I'd point out, though, that physically destroying the Institute would not accomplish this goal. If the powers-that-be still want a League, they'll just rebuild it. The League is an idea, not a physical thing. The League's fall would have to be political.
It's pretty easy to have the League collapse. Imagine if the US, China, and Russia all withdrew from the WTO. There wouldn't be a WTO anymore. Imagine if France and Germany left the EU. The EU would probably fall apart. Similarly, all it would take would be Demacia or Noxus getting pissed off and leaving the League.
In a non-stupid conception of the League, it doesn't have authority to rule on international matters because it's just so powerful that it can control everyone — it has authority because the nations of Valoran realized they were headed for total destruction if the Rune Wars went on any longer, and from that simple starting point it became an institution for resolving all kinds of conflicts, from trade disputes to wars.
Now, destroying the League poses problems. For example, Azir and Shurima? It's a cool setup, but from a cold-hearted realist perspective, without a League to defend its rights to self-determination Shurima would be instantly steamrolled by Noxus or Demacia, or would have to make itself a client-state of one of these superpowers. And, you know, it does involve removing the League of Legends from League of Legends, which is pretty stupid. Still, you could handwave something about how the Fields are still open for combat practice: it's just that the League has lost its authority to oversee disputes.