You can have sizeable homes even in walkable neighbourhoods. Look at any suburb constructed pre-WW2:
* https://www.google.com/maps/place/150+Geoffrey+St,+Toronto,+...
* https://www.google.com/maps/place/150+Westminster+Ave,+Toron...
* https://en.wikipedia.org/wiki/Streetcar_suburb
You still have a (back)yard and can have a garage attached to a laneway. Just up the street there are more modestly sized houses (3 bedrooms usually):
* https://www.google.com/maps/place/50+Geoffrey+St,+Toronto,+O...
Firstly, walkability only means higher prices if supply is limited. If it's the default, then supply matches demand.
Secondly, a grocery store needs say 500 potential customers (households) within walking/transit distance. A cafe 2,000. A specialist shop 5,000. Otherwise they need parking for customers arriving by car, which takes up yet more space, making the area less walkable, inducing more car demand and car lanes, etc. The same calculation applies to schools, parks and other amenities.
It isn't possible to reach those customer numbers while giving each family American suburbia levels of space.
Isn't it, though?
In fact, not only is it limited, it's also a market on the supply side.
> Secondly, a grocery store needs say 500 potential customers (households) within walking/transit distance.
In consolidated urban areas with medium density occupation, such as city centers in pretty much any relatively large European city, you already have multiple supermarkets at a stone's throw. In some places like Madrid some suburban areas even have multiple supermarkets on the same apartment block.
You might have your correlation/causation things mixed up. Walkability means higher quality of life, which means higher demand thus higher prices. In turn, as real estate prices go up, real estate developers are pressured to provide more houses from a limited construction area, thus this means shrinking apartment sizes.
Offering smaller apartments also has the advantage of increasing price per unit of area, while keeping selling prices within reach of the market segment you're targeting, i.e., you might not afford 1M for a house with 200m² but you might afford 500m for a house with 100m².