The problem arises when, in the pursuit of market share, everyone tries to compete on price. We have seen this happen ever since private airlines were allowed to fly on domestic routes. At one time we had as many as fifteen of them! Nine of them have since perished because, instead of adjusting quantities, they tried to lower fares. But this sort of price competition is futile because of something called Ramsey pricing which applies to networks. It’s named after Frank Ramsey, a mathematician of the last century.
There the objective of the firm is maximise revenue, not profit. While this works fine for monopolies, especially government monopolies, it’s disastrous for competitive markets which try to maximise both by minimising costs. This happens particularly with airlines. Usually, it’s safety that’s the main casualty, or wages and salaries.