Dell Medical School thought they could come in, simply exist, recruit "famous" docs and take patients from the rest of the city. Hasn't worked out well for them, as they are now losing hundreds of millions of dollars a year and are a ghost town. Any private equity group that tried to do the same would suffer the same fate, but they wouldn't have financial support from the taxpayer to do so. Baylor Scott + White does have a relatively robust program on the north side of town which has been moderately successful, however.
Austin has had many decades to grow and develop a very robust private practice infrastructure with very, very large private groups that operate very efficiently and control patient care in the city. Competition from academic medicine (up until Dell) was non-existent, and the two large hospital systems (three now) compete with each other for inpatient care but have not been able to make significant inroads into outpatient care, again because of how well-established pp is.
As a result, Austin has relatively few radoncs compared with other major metros, but that's because it's full of radoncs who are busy, not radoncs with 5-10 patients on treatment each supported by academic overbilling. Two clinics have closed in the last decade due to competitive pressure, and two radoncs have left the city in the last 4 years for the same reason. I have no doubt the radoncs in Austin would relish the opportunity to add a private-equity supported group to the list of casualties.