I know that this idea has been brought up before by other players. It has also become many mods.
Not really a follow-up of this post, but rather a further investigation of this suggested feature. The upcoming feature, Minecraft Realms, uses similar mechanics by hosting a local game via the Internet.
First of all, there has been high demands, mainly for LAN servers that are port-forwarded so that anyone can join, regardless where they are. I would agree that the LAN support was intended to be home network-only, but for people who like to easily start a new world and just host a server can use that method as stated above, Even though it is a much more easier way to just host a regular Minecraft Server. I had also noticed that even when the LAN world is closed by the default user on the local machine, it still constantly runs afterwards as 'LAN World', but no one will have access to it until the previous or new world has been opened to LAN. If the LAN server was just added regularly, it would appear normally as 'can't reach server'.
Second of all, whenever a new LAN Server is set up, the port will change every time. There is mods out there people can use to set the default port, but most of them do not work with modded clients, such as Feed The Beast and Tekkit. So, this would mean that you would have to port forward every time a new LAN world has started.
To summarize, this feature would be a great addition to the normal Start LAN screen. Many people have asked for it since Minecraft 1.3 and it would work well with the Mod API mainly, but as I said before, not really Minecraft Realms because of the similar mechanics. Also, commands like /op, /whitelist, /ban, /kick etc. would be useful.