Offline LANs have become commercially outdated
Server-based games are used as a marketing tool. Rather than having people play on their own, they remain connected to the company by playing on their server. Even if the server itself is free, the fact that they offer paid incentives on the server will gain them money from people playing on the server. If less people played on the server, there wouldn't be as large of a player base that would feel the need to purchase the incentives.
There are limitations to online servers. As some have posted, if a person wishes to have a LAN party, if the location doesn't have good bandwidth, they won't have a very good connection to the server. And to be honest, though others may disagree, I find games much more enjoyable when I'm in a room with friends, playing head to head with them, though Ventrillo and other team communication helps with that... Perhaps LoL should release in-game voice support? That's an idea for another day, however.
Anyways, despite the limitations, this allows more people to have better-quality games (though the LAN support could be implemented separately from the server, allowing both gameplay methods to work), allows the whole community to interact easier, and of course, gives Riot a good chance at making the money they deserve... and need.