Here's an idea. Make utility services scale with people density. Relax restrictions on how much they can profit off sqft. Single home dwellers are penalized with increased upkeep costs and higher density buildings are encouraged.
Utilities should be paid per-use, just as it is now. People with bigger houses are naturally going to pay more because a bigger house usually needs more power/fuel for HVAC, unless their house is more efficient. Also, we need to incentivize making homes more energy-efficient, and regressive policies like yours discourage efficiency. Smaller isn't always better; crappy old small houses and apartments can easily use far more energy than new McMansions.
And that leads me to one big problem in the rental market is that landlords never spend a dime on improving or renovating homes for better energy-efficiency, because the tenant has to pay all the utilities.
Maintenance is not going to be any higher for lower density; it's not like you see electric utility workers in the suburbs constantly, repairing stuff. And access is more difficult in higher-density housing too: in a suburb, you just drive the truck up to the transformer, but in a large building, it isn't that easy.
As for rural areas, there's a huge difference between urban and rural areas (where houses are miles apart), and urban and suburban areas (where houses are 20 feet apart).
If that were the case they could charge 'fixed utilities' at a reasonable price and then when they upgrade for energy efficiency they reap those gains.
Why not just have some kind of regulation requiring rental dwellings to meet certain energy efficiency standards? And combine this with some programs to help landlords upgrade, perhaps with low-interest loans or something.