The PE firm creates market demand for the goods/services that the purchased company used to provide at a better value to the customer.
So yes, the 'creation' is a demand which is sort of a destruction of the value that the customers previously had. In a fair market, this demand can be met. But a PE buys strategically such that this demand is not possible to satisfy because the company they purchased is entrenched in some way (regulation/monopoly).
It only works by having more capital to begin with.
Otherwise you wouldn't see consolidation where it shouldn't exist.