Yes? Wouldn't that mean that "the party" is over, just write a single paper and you can shut down and dismantle the machine you've just finished building?
Not hardly. If there was no Higgs, then some other mechanism would be needed to cause the same effects the Higgs does. We’d need the LHC even more then.
No, you keep running the machine, hoping to find a useful signal. More data means more fidelity. A lot of that has been probing the properties of the Higgs, but it's also spent a lot of time ruling out quite a lot of proposed extensions to the standard model.
The LHC wasn't built to discover the higgs. Another primary motivation was looking for supersymmetry and dark matter candidates. But really it was more general than that. Every time we've built a bigger collider we've found something new, and on some level, they just wanted to see what would happen. New data means new things to explain.