Healthcare providers are attractive to private equity 1) because of stable, non-cyclical cash flow, 2) benefits to scale (ie better negotiating leverage with payers), 3) ability to easily increase revenue at small clinics by "optimizing" billing (ie use more lucrative codes for the same procedure) and practice management (optimizing procedure mix and scheduling) and 4) regulatory protection -- local monopolies enjoy durable economic advantages and often are politically entrenched as healthcare providers are major employers
These factors aren't limited to private equity backed healthcare, though. Even non-profits take advantage of these things (sutter health in the bay area is an example). If you're looking for why US healthcare is so expensive, this isn't a bad place to start