Setting aside half our land is kind of absurd in that it's inevitably going to be undesirable land - look at Canada. The population clings to the boarder, so we preserve the boreal forest, but not the more southern parts.
If we create a grid pattern we either end up with a low general density where wildlife is free to move though our popylation or we end up with isolated areas of ultra high density (eliminating the urban sprawl) surrounded by nature allowing wildlife to freely move around our population.
My example is here in southern Ontario we generally don't see things like bears or wolves. However we can go south into the states to find them or north.
Southern Ontario homes 95% of Ontario's population and 35% of Canada's. Being from England where overpopulation wiped out many of the native species, being in southern Ontario feels the same. We're one of the least populated countries on the planet, but the Greater Toronto Area has an extremely high population density for how large of an area it covers. There literally is no room for anything bigger than a raccoon.
If we started developing rapid transit systems it would reduce the impact of confining urbanization.