As John Haine has pointed out, the old spinning disk meters did consume power, some of which you pay for and some you don't. Basically you pay for the I^2R loss in the current coil but don't pay for the V^2/R loss in the voltage coil.
Those meters don't charge for the reactive part of the load current, at least ideally. This is fair since the reactive part does not convey any power to you, nor does it cost the power company the full cost of the equivalent power. Why they don't like it is that the reactive current does cost them the loss in all the conductors leading to your house. So for instance if you have nothing connected in your house other than a large capacitor, there will be no net power delivered to your house, but there will be a reactive current flowing, and there will be losses in the power lines due to that current. Domestic users usually do not have enough reactive load to worry them very much, but in most countries the company has the right to insist that large users correct their power factor. It would be fair for the company to charge you something for having a very reactive load, but not the full V x A figure since that amount of real power is not having to be generated.
The power companies are also not all that keen on non linear loads like switch mode power supplies and vfd's, inverter welders and so on, which generally all present a rectifier to the power line. This means that they tend to take their current as a pulse at the peak of the AC waveform, which generates harmonics, which are not really welcome in the power distribution network. This can be alleviated by using a choke input filter on the DC side of the rectifier, but such chokes are bulky, heavy, and expensive so naturally do not form part of the usual circuits. Of course they will hate half wave rectifiers even more, these cause DC to flow in the secondary of the pole transformer. Too much DC will saturate the iron core, potentially causing a very high current to flow in the primary.
Here in NZ, if I put in solar power, I have to get a new meter. This is because if I am generating excess, the existing old style meter will not register any power fed back into the mains…that ratchet that someone mentioned above. So a smart meter in that case at least would mean that I did get paid for the power I supply to them, even if they only pay a miserable fraction of what they charge me for power going the other way. They only charge a quite reasonable installation cost for the new meter. I'd quite like to put in some solar cells, at the moment in the hot weather we have been getting I would be able to run the heat pump as a cooler in the daytime which would be very welcome. (Meanwhile in winter it sits idle as we have a wood burner which is much cheaper to run!)
John