Why would a unanimous decision on the Linda Brown case" carry more weight" than a divided one? In your own words

no one really purchased it themselves, it was all america, they had debates etc.

roosevelt essentially took the opposite approach as hoover in taking on the great depression. herbert hoover thought that america and its economy could naturally recover from the depression in due course, so he adamantly restrained the federal government from intervening on behalf of the people affected. on the other hand, roosevelt dramatically increased employment by expanding the federal government and establishing agencies that would aid in relieving some of the country's worst problems.