I've heard that said several times, but Blizzard says it's not true:
So, even though you have 2 computers 6 feet from each other on the same 100Mb or 1Gb network, everything will be running across your internet connection. I could see a LAN party of 6 people on a <2Gbps DSL connection running into problems with that. And if there's a 2-second blip in the internet connection, I'm guessing the last 1 hour you spent playing a game will be for naught.
Yes, people (such as I) still do this. My friends and I (usually 4-6 of us) get together about once a month to play Warcraft 3. I have another friend who goes to LAN parties for COD4.
I'm not sure how many people still play LANs, but I am certain that the only ones saying that "No LAN doesn't matter to me in the least" are those who don't go to LAN parties. It would be like BMW no longer making cars with manual transmissions. Would that affect the majority of BMW owners? No, and that majority would say, "Meh, it doesn't affect me, so I don't care." However, there are some big advocates for manual transmissions that would be in an uproar over it.
FWIW there are over 250,000 signatures for the
SC2 LAN Petition.