Well empirically lower demand does not lead to higher prices. The hopes and dreams of sustained profits are dashed by the coercive forces of competition. It's very sad.

That's not how it works.

Revenue is the area of the rectangle "price times volume". (Profit is "revenue minus costs".) Businesses want to maximize the area of that rectangle.

If a business thinks they can keep the area of that rectangle the same by increasing the price dimension, that will cause buyers to react by shrinking the volume dimension. That might yield the same effective area for the rectangle, but then also might not.