Aesthetically, it might seem more natural than asphalt, but lawns are a long way from ‘nature’. Realistically to have anything close to 'nature' assuming zero farming you’re looking at ~1 person per square mile if that.
Not sure I terribly agree with your person per square mile argument. Yes, lawns are a terrible waste (footnote: did you know that lawns trace back to medievel times? How much land you could afford to grow lawn on was a measure of wealth) and should be heavily disincentivized. But at the same time, if my house is zero net energy (solar power, solar thermal for water, tight envelope), and the transportation of myself and the goods I acquire are provided via renewable energy (electric cars/trucks powered by clean renewables), there isn't a strong argument against rural living.
The population trajectory appears to be ballistic, with us hitting the apex in the next 5-15 years (educated women have less children and prolong having children until later in life; almost all first world countries are already below replacement rate, India and China won't be far behind).
The problem is not population (or even food production) but energy consumption. But that effects our first world lifestyle so no one in the first world wants to take it seriously.
The first world is rapidly getting more efficient with regards to energy usage, and while I can't speak to the rest of the world, the US is quickly deploying renewables. With wind generation alone, we can supply 10x our annual energy consumption.
Enough sunlight hits the earth ever 5 minutes to power the entire world for a year. Its not an energy problem, its a capture and distribution problem.