it's going to happen. Or more likely we will start living underground so you still have countryside. Lots of possibilities and solutions. World wide we have hardly touched landmass. Even in England there's is loads of open fields compared to large cities.
Because open fields are natural?
Only something like 10% of UK landmass is actually natural, the rest is all man made baby, and you can see how just a slight change in the British landscape is affecting wildlife here, with extinctions galore already and hundreds/thousands of what used to be common animals/birds 50 years ago on the threatened/endangered list.
No, they may not be concrete yet but a lot of it is tantamount to it with respect to the affect on wildlife.
Now expand that globally, you have areas the size of Wales being deforested and turned into man made landscape every year, in just ONE country, even areas you think are pristene generally aren't. Travel across the US and you will notice, even though it has lots of space there is human activity almost everywhere. There is only a tiny percentage of pristene land left on Earth, and most of that is on Antarctica.
Even the seas and oceans are being affected, not just the overfishing and destruction of places like the North Sea, researchers have found affects as far away as the deep sea and abbysal plains, with beer cans found in km of water depth off the coast of the US and a huge area in the Pacific which is covered in plastic remnants (i'm talking thousands of square km). These in turn are affecting life not already threatened by fishing and other hunting activities.
Whales are a good example, within about 100 years whale populations collapsed, with extinctions and seriously threatened species only just surviving. A ban on hunting has helped but it will take hundreds of years to get back to their previous numbers, and even now Japan is complaining that the increase in Whales is a decrease in their fish stocks (how real that really is, well...).
Yes humans probably could survive with say 20 Billion people but earth would hardly be recognisable for those of today. I guess the only good things are I won't be here to see it and humans probably will be wiped out by something and the earth will only take a few million years to get back to a semblance of normality.