The word on its own is certainly too vague to be of much use to anyone. In its early days there was no problem with it. The Latin socius meant a partner, companion or chum, so societas was an alliance, or friendship, perhaps involving a good old gossip over a meal or a glass, after which people said how much they'd enjoyed each other's society. The point here was that the people concerned knew each other. Even when they didn't, it was reasonable to talk about "society" as a group of people, even a whole nation, who shared the same views on life, as they were more or less supposed to do when the word was thus used in the 17th century. Of course we are still a society in the sense that we're all bound by the same laws, a point neglected by Margaret Thatcher, but this won't help Mr Mandelson now that the Dome looks like being partly sponsored by the Japanese.
The wider its application the less it means. One can understand, while not necessarily applauding, attempts to narrow it down, as carriage folk did when they decided that society consisted only of themselves, and you could enter it, be shunned by it or take it by storm.
But I somehow can't see Greenwich becoming a society venue.