The problem isn't that the city is full. It's that suburbs are made for cars.
You could have suburbs designed as walkable neighbourhoods with shops. Look at Japan, each area around a station is like a small village. Even if you commute to the "big" city, the area you live can still be a nice walkable place.
I'd go further and say that modern suburbs are designed to completely isolate commerce from residence, in a way that doesn't just necessitate driving, it necessitates driving long distances to centralized commercial centers. So you can't just walk around the corner to a shop and get what you need, you have to drive, sometimes for miles, to get to a big-box grocery store. And because people didn't want to drive all that way for one set of things, just to drive another long distance for another set of things, you ended up with clusters of shops (or more frequently, clusters of big box stores), all in these centralized locations.
You can see this all over the east Bay in the San Francisco Bay Area, where its just miles and miles of residences, with all of the commerce on 880, 580, or all the various names for 185/238, from Gilroy to Vallejo. If you're more than a few blocks from any of those roads, you're driving or taking a bus to get to any shops. And East Bay surface streets are not exactly pleasant.
You often can "go down the block" for some value of "block" (often within walking distance, if not perfect walking conditions; definitely within bike range) but the store you find is likely expensive, small, and limited. The same time expenditure gets you to Walmart (or Target, if you're upmarket) and things are more plentiful and cheaper.
The funny thing about the big box stores is that they can apply so much pressure to their suppliers (and their landlords) that the price difference outstrips differences in quality and convenience.
Once upon a time I lived within easy walking distance of my job, a big box retail store in one of these clusters. Elsewhere in the same cluster was a Market of Choice, which is basically a Whole Foods but for Oregon residents who are too cool for such a mainstream store. Despite the higher costs, I vastly preferred shopping at Market of Choice because I could easily walk there and the food was generally higher quality. Generically, I would consistently shop at stores I could bike or walk to, outside of that shopping center, and frequent restaurants I could get to.
Meanwhile, where I live now, there's a Haggen (an Albertson's branded Whole Foods competitor) across the street from a Safeway (which is the brand Albertson's uses in this particular market for their standard store). They carry identical store-brand items, but the premium store charges 5-10%, because they know that people will pay more just for a better shopping experience.
Obviously I don't speak for everybody, but I think a lot more people would accept paying a little bit more in exchange for not driving so much, but part of the problem is that, thanks to market effects and economies of scale and so on and so forth, they have to pay a lot more, for the same products.
Isn't the issue that there are zoning laws preventing the conversion of the suburbs into more city?