I wouldn't spend that much on a single item, but I live in the red-neck rust belt. It might be a reasonable thing to do someplace more urban. But spending money on decent looking clothes, even pricey clothes is a no-brainer if you don't want to be treated like white trash (or whatever group people want to put you in). They probably aren't ever going to see your house and they might not see your car, but they will see how you look and hear how you talk, so that stuff matters.
You have to be halfway believably like them or they will have trouble seeing you as a human being and the same thing will go for your kids. In my area, that means JC Penney and Shoe Carnival for the kids. You don't have to go brand name on the clothes, but you do on the shoes. At least at the poor schools my kids went to.
And you don't want to get flashy designer stuff because the elementary teachers here are almost all middle class white women whose husbands and dads do blue collar work or are teachers themselves. They can't afford the flashy stuff and resent when "poor people" have it. You want to be seen as 'deserving poor' not those other people. It sucks, but that's how people are.