I think in theory it does, but in practice the customers of PE-bought companies don't update their priors fast enough.

If a company being purchased by PE meant that they lost the vast majority of their customers as soon as contractually possible, then the possible value extracted by PE would drop off a cliff.

This isn't necessarily the fault of the customers - we're all dealing with a lot of information to process.

And, up until recently, it was reasonable to attach reputation to brand instead of to owners.

And I think that's a lot of what PE exploits - the gap between people's belief about a brand's reliability/reputation, and the fact that the actual reliability has been a function of who the actual owners of the company are for many years - but people are still attached to the old mental model.

(there may also be some value for PE to extract from assets aside from customer relationships and the higher-order "brand value", but I suspect that that's secondary - if I'm wrong please correct me)