That said, in the US, many people (Asians included) can go to shitty schools and still succeed. Their success is despite the formal education they got at a low SES school, not because of it.
Generally when you see elite school success from students from low-SES areas, it is due to substantial intervention at home and/or extracurricular education/tutoring.
You ask why it is a handicap. If they could get quality education during school hours, their extracurricular hours could be used for deeper study or more interesting endeavors (e.g., research projects).