Psychiatric wards in the U.S. are for very short term stays by people who have extreme problems. They take people who are at major risk of causing harm, and patch them up just enough so that they can be thrown out. And even that is being scaled down and sped up.
The inpatient mental health system is like a mental ICU: designed for prevention of death, not for anyone's convenience.
My point is that this approach causes harm. It's like treating heavy bleeding by applying a tourniquet and sending the patient out the door. It's medically unsafe, unsustainable patient care. This is not simply a question of budgets, it is a question of how society views mental health. This kind of treatment indicates an "us and them" mentality where mental patients are viewed as second-class citizens. Your wording, "extreme problems" also hints at such a dichtomy, although I'm sure you didn't do it on purpose. There are other ways to say this: Basket cases, crazy, insane, psycho, major issues, etc. A neutral term would be "very ill" or something like that.
My examples of attempted suicide by overdose or "self-influcted gunshot wounds" definitely qualify as "extreme problems", so it is clear that there is a different way to do this.
I am aware that your comment probably just meant to say that the system is set up in an unfortunate way, and that you probably don't represent the views I describe here. But from my perspective it appears to be much worse than just an underfunded system.
The inpatient mental health system is like a mental ICU: designed for prevention of death, not for anyone's convenience.