Rent-seeking is the name for what happens when middlemen insert themselves somewhere where they're not needed, but do it just so that they can charge money for the “service”.

Health insurance providers are middlemen in the transaction between healthcare services and people who need those services. But they wouldn't “need” to exist if their homespun and arcane systems of “networks” and “coverage” didn't exist.

At this point, it makes sense to have someone filling that role, but only because of institutional inertia. Single-payer is so great because it doesn't fight against this inertia, but embraces it, telling the insurance companies that sure, they can keep operating as private entities, but in order to do so you may only interact with a single entity through which all payment for services is sent. If they won't make a deal with that single payer (the government), then they get no payers. This reintroduces bargaining power on the part of the people, instead of the case now where we are “forced” to pay the “rent” that healthcare is “seeking” just by virtue of them being in a position to withhold the service if you cannot pay.