Chicago quickly drops off past the 20k/sq-mi range too, which is basically typical rowhouse density. It only has 88,000 people living in >50k/sq-mi census tracts, mostly stretched out along the northern waterfront. Amsterdam has almost twice as many at 162,330.
Amsterdam isn't even that dense by European standards, although Swiss cities are probably similar. The densest cities are in southern Europe, ex Valencia has about 800,000 residents over 20k/sq-mi, and 400,000 residents living at 50k/sq-mi densities and it's not even a big city. https://chartingtransport.com/2015/11/26/comparing-the-densi...
But back to the original point... Chicago has fairly dense areas within a short commute of downtown - but those mostly have 2-3 flats and bigger apartments, and the few single family homes are quite expensive. For more affordable SFHs with a decent school and crime situation, I think you'd have to go to neighbourhoods that would be considered "suburbs" by European standards even if they're within city limits.
San Francisco is even more expense, the better neighbourhoods have SFHs at $2m+. More far flung areas like Sunset would be more like $1m which is still not exactly cheap and it's getting to be a long commute (40-50min each way by transit).
I'm getting the impression that Europeans would "call them suburbs" because they have affordable single-family houses in them, which makes this debate pretty disingenuous.
Chicago neighborhoods like Edgewater are in the 30-35k/square mile range, and are full of little single family homes with yards. That's well into walkable territory.
Chicago has between 1.1-1.3 million people (twice as many) living at that density or higher: https://lh6.googleusercontent.com/-Z3ai_T6K_40/T4I6B9akQDI/A.... It's actually more than that, because this data excludes satellite cities, which the Amsterdam figure above includes.
Another point of comparison. Chicago the city has 2.7 million people at about the same weighted density (19k/sq-mi) as the Amsterdam metro, which has 1.7 million people.
EDIT: these are not my charts. They're from this thread: http://forum.skyscraperpage.com/showthread.php?t=198004.