Maybe I’m misunderstanding the US situation you’re comparing to, and people there just build flat, so even a few floors is already building up? That would be strange though...
I specifically don't mean that you have to build up to Manhattan levels to get walkability. Personally, I find the skyscraper jungle of Manhattan to be a nice place to visit, but I wouldn't want to live there, at least at my stage in life.
If anything, perhaps Manhattan levels of density are not great for nice retail businesses. If the average building is 8-10 stories, there is relatively little ground level space available, rents are high, and so there is little room for experimentation. The 5-6 story Berlin (and to some degree Paris) level of density is maybe a sweet spot.
Now, this doesn't necessarily work as well for families with children. However, Berlin manages to be decent for this by having very wide sidewalks, a lot of parks, and hinterhofen. Some parts of Chicago and Brooklyn manage to achieve a similar effect with single family housing by having tightly spaced three story row houses.
Like I said, ultimately a lot of cities that are nice to live in in this way are that way because they were built before the invention of the car, so people valued this much more than they do today when the alternative is to get in their car and go to some big box store with a huge parking lot that doesn't need to be very near by.
If Paris is a model for the world, I don't want this world.
Numbers from https://versus.com/en/berlin-vs-london-vs-new-york-vs-paris/....
Edit: And a considerable amount of land given over to parks, museums, churches, and other non-residential spaces.
So yeah, Paris is dense, but if you compare block by block the differences are smaller.
[1] https://de.wikipedia.org/wiki/Verwaltungsgliederung_Berlins
Yes, that's exactly the situation in most neighborhoods in the U.S. One or two story single-family homes with large setbacks on all sides.
A 5-6 storey standard would likely more thaan double SF's housing capaacity.
At the time the buildings were constructed, 5-6 storeys was a practical limit.
Not just people, but food, water, and waste travelled by stair (or, in the latter case often, air).
What this means in practice is you don't build between 6 and 10 floor buildings because the numbers won't work out. (obviously there are exceptions)
The best for walkability was Berlin, which, in the inner part, is mostly 5-6 story buildings. Within two blocks there were numerous stores and about 8 restaurants and a few bars. I also lived in an older suburb of mostly single family houses, but the lots weren't that big, and every house was two stories.
The key to walkability is that you need density. For a business to get much foot traffic, you need a good population in the walkable catchment area, and for that you need density. To get density, you need to build up. Unfortunately, building up is more expensive. Another thing that's helpful is alleys. If you put the garage behind the house, you don't need as much frontage width for driveways and garage doors.