There are many open questions about the mechanism(s) behind them, as well as the extremely frustrating fact that we can never truly tell if we are actually seeing the surfaces of multiple completely separate underlying pathologies that result in somewhat related loose symptom profile clusters.
But if we were to take an extreme example I encountered, a person whose life was basically over to the point of him trying to butcher people over his delusions[1], and you find a medication with which he can regain control of his own mind, can live in society rather than prison, even hold down a job and have fulfilling friendships, and over months you see numerous patients with this same dramatic reduction in symptoms, there is no question that there must be underlying pathology at play.
There might be numerous underlying pathologies all fitting the same symptom cluster, which would (potentially) help explain why even on the same symptom cluster a medication might have drastically different levels of effectiveness on different people.
The best reason to think underlying pathologies behind psychiatric illnesses are real isn't that we have clear the biology behind them, but that there exist treatments that actually have very measurable effects on the symptoms. The other reason is that we already concede our thoughts and perceptions themselves have a biological basis, so it would just be profoundly strange if 'disorders of thought and perception' somehow didn't.
[1] Just an additional note here, I'm using a specific example of a patient with violent delusions and criminal behavior, but it's important to note that people with mental illness are much more likely to be the victims of violence than perpetrators of it, and it is important we counter the unfair stereotype that mentally ill people are prone to violence.