Who gets intensive psychotherapy?

Severe illness. A best practice for cognitive psychotherapy for someone with depression whose depression and anxiety worsen is to increase the frequency of sessions/increase intensity. Generally, more intensive psychotherapy is helpful for those with severe, worsening, or relatively acute symptoms/conditions.
Varies. Intensive psychotherapy may be more beneficial than other kinds of treatment when a condition is acutely serious, like early stages of recovery from addiction, or when a condition has become chronic as a result of personality factors, etc.
Intensive therapy. Unfortunately, intensive is a word which has been associated with either challenging or "aggressive" pursuit of information. In reality, all types of psychotherapies should be applied intensively in order to best help the patient.
That depends. There can be intensive programs such as partial hospitalization programs for individuals dealing with serious illness. However, intensive can also refer to frequency of sessions or depth of treatment. In that situation - it is usually someone is very motivated (and who has the money to afford any costs that are not covered by insurance).
Severity of symptoma. Typically those with the more severe or otherwise life threatening pathology receive more intensive psychotherapy. An exception to this is analysis that is undergone by those in analytic training, where sessions can be three or more times a week, and this can last for years as part of developing as a psychoanalyst.
No general answer. "intensive" has no standard, agreed-upon meaning. In practice, it has come to mean anything that a health insurance company doesn't want to pay for, and can claim is not a "medical necessity." frequency of sessions should depend on what therapist and patient want to accomplish-- e.g., self-knowledge and insight, versus symptom relief-- not necessarily on diagnosis or severity of symptoms.