I have no words for how completely toxic the surge of PE in healthcare has been. It's driven the degradation of care everywhere I've been. Healthcare chains have no issues with investment (see any annual reporting document to see how much money is sitting in various investments, mostly RE); smaller clinics being eaten up by PE chains is not an answer to centralization, it's just another mechanism of it.
"Private equity" also includes venture capital here. It means all private direct investment. The thing you are imagining is one small corner of what private equity actually is.