I'll try to address the useful and meaningful part of the question.
In USA specifically, the primary (K-12) school educucational system is in large part funded by local property taxes assessed on people and businesses in a specific locality (town, borough, county, state).
In addition, a smaller factor is that local PTA fundraising drives supplement a lot of items in school budget; which presumably a bussed-in poor students' family would also fail to contribute to yet benefits from.
As such, going to a school which is outside of your local area of residence is basically equivalent of stealing the money of the people who live in the area where you go to school to, since THEY pay for your education, instead of your family doing so.
Does this have an effect on inequality? Somewhat. However, the effect is significantly less than people who loudly proclaim to "care" about inequality state, since both historical practice, anecdotale evidence, AND research indicate that the main predictor of success in school is NOT money, but:
The level of engagement of the students' parents - which going to a better far-away school may be correlated to but isn't caused by
Lack of hunger - which is 100% addressed in USA on federal and state level by providing taxpayer-paid food to all poor kids in school
... and, very specifically, NOT the amount of money spent per student, above a certain basic level (the state of New Jersey demonstrates that conclusively).
The only factor that matters in terms of transferring school, but isn't typically addressed by research due to political correctness considerations, is cultural. If a smart minority student is surrounded by his peers who pejoratively call doing homework and studying "acting white", it actually has detrimental effect - bad enough that Barack Obama spoke out against the idea.