I recommend to people the Tenement Museum for their second trip to NYC - it was eye opening (but pretty grim)
You have no money, very little skills, you don't speak English. Even if you cobbled together money to take the train to some small town in Ohio or Iowa or something, what are you going to do as a complete social outsider who doesn't speak the language?
The idea was to stick around in the LES where you had an actual community. Try to make some money, learn English, develop some skills, and then move out. Which is exactly what people did. And the new immigrants took their places.
Also -- they had already fled. This was the fleeing. From Ireland, from Italy, from Poland, etc.
It’s still happening today.
That aside, that there was literally no going back, given the travel to get to NY. I had an ancestor come to NYC in the 19th c. and return back to Sweden, but he was not in the desperate straits that many were. I'm sure some would have returned, given the opportunity.
You see it time and time again.
There is a good argument that San Francisco could and should be denser than it is, but its ludicrous to call it not dense at all.
quick funny story, my family and i were in Times Square last year for New Year's. Thousands of people everywhere as you can imagine. We're walking down the sidewalk and right as rain my wife runs into someone she knows from all the way back in Texas. Among all those people from all over the world she still manages to run into someone she knows. My wife and her talk while me and the boys hang around waiting just like we've had to do at our local grocery store back home. My kids and I still laugh at that story.
They have a population of 6 to 7 million people in an area of 700 square kilometers, resulting in a population density of 8300 people / km^2. Substantially more than that if you account for the fact that a large percentage of the island is still tropical jungle.
Despite that fact, their city planning is so good with large open spaces everywhere interspersed with greenery, that you almost never feel claustrophobic. Even the so-called "hearland" neighbourhoods with rows after rows of high-rise residential HDB buildings are quite pleasant.
The most claustrophobic place I've been in Singapore are the few squares in the center of CBD filled with skyscrapers that almost obscure you the view of the sky.