I think the key isn't so much making the single-family homes more dense, but allowing more mixed development mixed into the larger neighborhoods.
Take my neighborhood (south Reston, VA). The main road is about 2.5 miles long. There is a strip mall at both ends, leaving homes in the midde just outside easy walking distance (from my house, by footpath, it's nearly 2 miles to one end and a bit over 1.25 to the other). There is a major intersection about halfway down that main road. Instead of allowing a small shopping area, it's more houses. Hard to change now, but if it had been zoned mixed-use/light commercial at build time, there could be a coffee shop and small grocer there. And bring between 1/3 and 1/2 of the available customers in the area within walking distance of at least some of their regular errands.
Additional benefit of this would be reducing the size of the malls at each end, mostly by removing parking spaces, freeing that space for townhouse, apartments, or more shops.
Take my office... it's 1.25 miles away, and I walk. But, the complex is all offices. If there were a grocer there or on the way, I could eliminate my 1x weekly carload, instead grabbing things as-needed on my walk home.
Same office. I have coworkers who live closer than me, but refuse to try walking because the sidewalks and street crossings from their direction are less user-friendly. Crossing on/off ramps without signals. Crossing a 4 lane highway with 50mph traffic. Etc. Some simple crosswalk modifications could make the office complex walkable to some of these coworkers. But, traffic planners don't even appear to think of these things when building roads - it's almost 100% car-focused.