In Norway we pay three different amounts, sometimes to two separate entities.

I pay the company that supplies the electricity per kilowatt-hour for the energy and the company that owns the local distribution network for the rental of the cables and a per kilowatt-hour fee for transporting the energy.

In my case it is just one company but the energy supplier could be separate from the infrastructure owner.

This kind of "free market" for electricity tends to drive up infrastructure costs needlessly (see Australia), while incentivizing bad behaviour by generation suppliers in the market (see Enron).

Public utilities generally provide a higher caliber of service at a lower price, with less administrative bloat.

Depends on the state, but in Vic the 'poles and wires' component, both in distribution (suburb) and transmission (pylons) costs are built into the fee that is charged for electricity supply (cost of connectivity) in a positive feedback loop: the more the companies invested, the more they could charge.

This was designed to avoid the 'run it into the ground's privatisation mentality, but it went the other way. Sadly, there was no price component for improving the network with new ideas, so it is still the same design as 100 years ago.

A system designed by accountants has done things accountants love, and nothing for electrical engineering or the citizens. Surprise.

The old SEC wasn't innovative or cheap, and neither is the privatised system. For incentives to be effective they have to be broken down to be smaller components rewarding specific conduct, and tweaked in response to system performance.

The ownership of utilities and the cost of their infrastructure investments has nothing to do with the 'freeness' of electricity markets.

The performance of utilities is more a function of regulatory power and willingness to regulate rather than utility ownership.

Please tell me it’s at least coordinated enough that the two entities send it together on one bill.

Usually it's one bill. But even if it weren't it's not a problem because the bill goes straight to my bank and I pay by direct debit. The bank notifies me in plenty of time by email. We don't use paper bills and invoices much in Norway any more. After the first one or two from a new supplier most people switch to email billing and direct debit (eFaktura and Avtalegiro).

I just get one bill, even though in my case it's two companies (because I shopped around)

It’s more important to subsidize new technologies. Now that solar panels have a foothold, the economic case has gotten dramatically stronger because they’re cheaper. Even if electric bills change, I thinks uptake would continue.