Although it does drive costs up, profitable hospitals are what ensures a high quality of care for patients. If hospitals don't take good care of their patients, bad reviews, complaints, and legal action will cause them to lose business. When hospitals rely on the business for profit, they have a strong incentive to provide a good service to their patients so they can continue making money. If hospitals were not for profit, the personal incentive to the doctors, nurses, and workers would not be performing their job well and patients would not receive care at the same level.
There have also been many established research papers and analyses done which proved that government-controlled hospitals simply won't work. Given the complex nature of the American healthcare system, governments would prove inefficient and insufficient in understanding the complexities of the field. It is better managed by private hands, and ultimately the for-profit model motivates doctors and workers to provide top-notch services.