Are people generally hospitalized for delirium?

If acute and serious: There are many causes for delirium. Most common would be drug toxicity. This can be very serious and need acute medical care. Withdrawal from alcohol produces delirium that can cause serious medical complications. Infections of the brain can present with delirium and progress to coma. Patients with long standing psychiatric disease or dementia do not need hospitalization.

Often, yes: By definition, delirium is an acute change in mental status characterized by altered alertness, focusing ability, and activity level; confusion; disorientation to time ; place, etc; decreased short-term recall; disrupted attention; disorganized thinking, etc. Medications and drugs (including withdrawal) are common causes, but so are infections ; many other medical causes needing acute treatment.