It will seem unrelated at first but in EU it is usually considered that you can enter the EU if you are approximatively geographically attached to the rest of the Union and have most requirements to be considered a developped country (altough it's sometimes realy questionnable).
Given the enormous amount of underlying issues in US that are part of its foundations (as exposed in the OP), so appart from the GDP US in this highly hypothetical situation might be refused, thus considered "not a fully developped country".
I'd like to add that equality in the eyes of justice should be a requirement for developped country. Given the very well known racial bias in the US justice system (Though France is also concerned for example) and that one of the most important court in the US (immigration court) does not give a right to free counseling, it's two more reasons for the US status as a developped country to be questionned.
Given Gdp per capita that of the US is twice as high as most European countries. Also so is the debt per capita. As for the racial tensions and bias those are very present in Europe also, just in a different way. Just watch the tensionsbetween Turkey and NL/Germany for example. Same goes for sexism in that regard if you are a male you will probably get a harsher punishment for the same crime.