To a large extent who takes care of sicker patients depends on where you practice. If you work exclusively in an outpatient surgery center or an office based-practice you are unlikely to see anyone sicker than an ASA III. (Most ambulatory surgery centers turf these cases elsewhere.) Some community hospitals do not offer surgery for cardiac, neuro, trauma, thoracic, etc. (You will, however, see an ASA IV patient present for a total hip replacement or colon resection in this environment.)
Critical Care Fellowship is for people who genuinely love managing a critically ill patient in the ICU environment. (Many of us non-intensivists admire their work but cannot personally stomach working in the ICU environment.) Anesthesia-trained intensivists in academic settings often have subspeciality interests that steer their OR time towards the care of trauma, cardiac, transplant, thoracic, neuro, and other potentially complex patients. One does not, however, need critical care training to do these cases in most locations. Finally, any general anesthesiologist in a hospital with an ICU should be able to manage an ICU patient who comes to the OR for routine procedures (Trach, Exp Lap, Burn Care, etc.)
