LAN Parties. Could they be better?

A little context first: I have a lot of friends who play League, and when we're hanging out together we usually like to play a few games together as a 5-man premade. But the internet we play on seems to be just slightly too weak to support 5 of us without occasional lag and sometimes disconnects. It's always a risk to play with a full 5-man team. I don't know how common this problem is, but I would think that there are a good number of friend-groups with similar LAN-party issues.

So that got me thinking. League isn't terribly demanding, but when there are five people on the same internet connection... well it's 5 times more work. But a lot of that work, a lot of the information sent over the net-tubes, is duplicate info, right? If all five of us are in the same match, the server is gonna send us 5 copies of the same info telling our clients what's going on in the match. If that redundancy could be eliminated, then we wouldn't need nearly as much bandwidth and our humble LAN party wouldn't lag anymore.

So here's my theory. We're all on the same network, connected to the internet (and each other!) via a router. What if one of our game clients was given the special role of "intermediary host", and that client has the job of receiving all this redundant info from the servers and then dishing it out over the local network to the rest of the clients.

...Okay, I somehow fit my whole idea in one sentence and that doesn't seem very clear. So I'mma break it down:

1. Me and 4 friends are on the same LAN and we start a League match together.
2. During the match, the server is constantly sending data about the game to our clients. Much of this data is redundant because we are all in the same game, and all of our clients need to know things like "Where are all the enemies that we can see?"
3. The server sends the redundant data to only one of our clients, which I'll call the "host"
4. The "host" client receives all the data normally, but then relays the redundant info over the local network to the other 4 clients.

This way of relaying the redundant data would cut down on the data that has to be sent over our internet connection, but it would mean our router would have to work a little harder (I think it can handle it) and the 4 non-host clients would get the data, slightly slower (<30 ms??).

So uh, that's all I have. But the reason I'm sharing in the first place, is because I'm curious if this is actually a feasible and/or useful technology. Is it possible to improve the quality of LAN parties in this way, or in some other way? If LAN parties could be improved, how many people would actually benefit from it? How many people out there would like to see something like this be implemented? Any and all comments/suggestions/discussion is welcome.