Only lower demand could potentially translate into lower ticket prices. Why would a company lower prices (and profit) if people fly anyway at current prices?

See https://en.wikipedia.org/wiki/Effect_of_low-cost_airlines_on...

Lower price is caused by another airline offering the same flight for less.

A cheaper flight enables for this to happen, but does not guarantee it.

well cheaper for the airline can lower the floor price. At some point it's no longer possible to make a profit at all, and over time the airline has to recognize that or go bankrupt