It's not even really a trade-off because at the end of the day both live in the same country. The friction and dysfunction that is caused by this division also shrinks the space of the top 20%, who end up in a golden cage at best.

I'm German from a low income family and I went to school with kids of millionaires and everyone walked through the same streets and went to the same bars. First time i went to the US I noticed what living in a bubble actually means. And the kids of the 'winners' seemed as neurotic as the kids of the 'losers'. There's an entire mindset of "if I not go into college X will I be where my parents are", "is such and such street safe", "should we move to X neighbourhood, is it better than Y". Even the "opportunities" that the people in the top 20% is basically are pure stress.

"both live in the same country"

Yes, but that country is fairly huge. Even in densely populated Central Europe, we tend to make fun of sheltered kids from posh neighbourhoods (how many low income kids are there in schools of Nobelviertel, Hamburg? Perhaps a few well-chosen refugees). This effect is ten times stronger in the U.S.

I am not saying that this is right, just a description of the state.

BTW Unsafe streets are definitely a thing in Germany (or Czechia, for that purpose) as well. No one will, for example, move voluntarily to a neighbourhood with a high percentage of Roma population, regardless of how anti-racist was their education. Or to the proximity of a well-known drug dealing space. European hard drug problem is quite acute in some hotspots.