Lots of people ask to be admitted to hospital every day. Far far more than we would ever have beds to contain so we have to make choices on the basis of risk: benefit and because we are humans and the future is hard to predict we sometimes get it wrong.
If someone is harmed do you really think it has no impact on the psychiatrist and they don't care? Of course we do. Again we are human.
If someone is badly harmed as the result of a poor judgment then there will 100% be an official investigation. That could be internal or external if the harm is very bad. If it's suicide you can expect a trip to the coroners court to explain yourself to the coroner on the public record. This is every psychiatrists worst nightmare. Of course there are consequences if we are wrong. It's just totally wrong to say there aren't and we are all acutely aware of those.
Most people ask to be admitted mainly in order to feel safe because they believe that can't manage how they are feeling themselves.
Sometimes it would be wrong to agree to this because
For some conditions (especially medication non responsive ones) admission is only a short term respite and doesn't make any long term difference
If a person is admitted every time they feel they can't cope then this becomes their default option and their only coping strategy and they never learn any better strategies or develop community support networks because they are always just admitted (briefly) to hospital
They may in fact be better off in the long term to learn ways to cope with their symptoms without admission
Mental health hospitals are usually not a haven of peace and tranquillity sadly. They are full of people who are floridly psychotic, manic and behaviourally disturbed all crammed in one space. At any one time it's pretty likely at least one person will be creating a disturbance, shouting, not sleeping, behaving in an alarming way.
Admission is highly likely to happen for florid psychosis and mania as these conditions often can't be safely managed outside hospital and require medication treatment
Admission is highly unlikely to be offered for personality disorder because this requires long term psychotherapy which is not available in hospital.
For other conditions eg depression it really depends on the severity and risk but it is always a last resort and usually medication will one of the main purposes. Yes there will be OT groups, short term group psychology and nursing but fundamentally you would not be admitted just for those unless it was to a very specialised unit eg a personality disorder unit would have a commitment of many months