Why don't they increase the price or create another higher tier, then? With so much "demand", they would make a lot of money.

Because then Anthropic would have to guarantee that those customers would actually get the service they're paying for.

At first it might be just a few customers on that higher plan, but it could quickly grow beyond what Anthropic could keep up with. Then Anthropic would have the problem that they couldn't deliver what those people would be paying for.

It's very likely that Anthropic is not short of capacity because they wouldn't have the money to get more, but because that capacity is not easy to get overnight in such big quantities.