The biggest defense of LANS I can think of is that a lot of people want to be able to play with specific other people. For example in my house we have 3 seperate computers networked together (mine, my father's, and my stepmothers). If we ever wanted to get into RTS games and play against each other we would of course want to be able to do it using the household network.
It's also notable that in SOME (admittedly increasingly rare) jobs, you have teams of techies who are there simply to be on call, and the bosses really don't care if they kill time "on the clock" as long as they come when needed. In certain cases you might see "office LAN parties" constantly ongoing. They might not care about people playing over the LAN but not wanting people to be playing things using an outside connection for security reasons.
Both of these kinds of things are audiences Blizzard will alienate.
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HOWEVER, also look at this from another practical perspective:
People use LANS to make money off their game from which they do not receive a cut.
In the US this is fairly humble, a computer store owner or whatever might host a contest as a promotion for his store. Any competitive game will work, but something like Starcraft is going to be a popular choice since so many people play it. The store charges so much money to enter, and then gives out a prize to the winner, oftentimes making a profit off of the admissions, a profit which Blizzard sees no cut of.
On the extreme end you still have a few "net Cafes" where people go specifically to gamble based on video games (ie admission fees which make profits for the house, and then a chance of making more money than the admission fee by managing to win a nightly contest, or due to side bets conducted on a game's outcome). This is not only illegal in most parts of the US (despite minimal attention being paid to it), but again it's money that Blizzard gets no part of.
In general the US part of the equasion is so tiny that Blizzard probably doesn't care. *BUT* when you get into the insane population of Asia where gaming is becoming what amounts to a professional sport, it becomes a big bloody deal due to the amount of money involved. Blizzard probably has deals going (one way or another) with some of the more public/open competitions, but not from the lesser and more private ones.
Removing LAN play allows them to better monitor the game's usage (so they can track things and hopefully make sure they get more of a cut from what is going on), and also provides some leverage in countries with more "obtuse" laws than the US. Right now in asia it can be argued that since the game supports LAN play and what they are doing is not inherantly illegal, they are just using the software "as intended" and Blizzard isn't entitled to anything other than the money they spent for the software. But on the other hand if they have to modify the game illegally (use it as not intended) to run it on a private LAN, that changes things.
Basically I think Blizzard pretty much wants to get as tight a control of the multiplayer as possible so they can milk competitive Starcraft.
Also it should be noted that Blizzard thinks they are a big honking deal (albeit not without reason). They have long-term plans revolving around things like a "Blizzscore" which will allegedly affect things like bonus content for long-term fans in their newer gamers and such. This is tied into your Battle.net account. Currently it's measured as achievements in WoW which is their first game to support it.
While a lesser issue than the money above, consider that if they are taking this seriously, they don't want people using a LAN to be able to cheat on Starcraft Achievements, especially if the Blizzscore will eventually mean more than a Microsoft "Achievement Points" score at least when dealing with their products. In some ways thinking further ahead (and learning from) Microsoft and Sony's implementation of their system, where people have used "offline multiplayer" type features to pad their scores without actual online competition.
My cumulative thoughts, the biggest point though is that I think they want to force Asia onto Battle.net more, and get as much leverage as they can (practically, and legally) to start sucking money directly from the jugular of SC competitions.
