The owner of a company can make a big difference in its value. A PE firm can often bring in expertise to increase profits in ways that the current owners can’t, for example by increasing reimbursement, optimizing revenue cycle, or reducing expenses. Often other companies in the firms portfolio help augment this. These methods are not artificially pumping up value - they actually make the company more profitable and therefore more valuable. Sometimes they can be exploitative - like air medical transport companies that have used surprise medical billing to pump up revenue. Sometimes they just take advantage of underlying trends, like acquiring a CMG in anticipation of physician oversupply reducing labor costs. There are some shady tactics that give PE a bad name but in at least some cases, they genuinely improve companies after acquisition.
You are absolutely correct. There are a few bad actors that are value destructive that create a bad name for the entire industry. Personally, I don't think there is much value in health service LBOs, ie Envision, TeamHealth, HCA. These are big companies and I'm not sure levering them up with debt is going to make clinical care any better. On the other end of the spectrum, there are many high quality single or multi specialty practices that benefit from operationalization and can grow and offer better clinical care as a more integrated organization. This is where earlier stage growth style PE is very useful.
I certainly wouldn't call any proper reputable PE funds or hedge funds I know ponzi schemes. That implies a specific model of disbursing money with inflows without generating any gains. Some funds aren't good investments and can lose money, but not ponzi schemes. Some other funds are ponzi schemes, but very few and far between.
The discussion of whether a capitalist economy can function without these players is a whole other discussion. Yes and no. In public markets, hedge funds inject significant liquidity to keep the wheels of equity markets nice and lubricated. Do they also sometimes have a negative impact? Absolutely. Too much nuance to really discuss here.
One area where hedge funds are critical is in drug development. A lot of middle and late stage drug development in biotech companies is financed by the equity markets in which hedge funds are some of the primary financiers. Without many of these biotech focused funds, much of drug development would slow significantly. At the same time, does this lead to a potential misprioritization of which drugs to develop? Absolutely. Is there a better way? I wish, but not readily available at the moment.