Not all colleges have application fees, including some selective ones. As for having totally blind applications, most colleges want diverse student bodies, including geographic, racial and socioeconomic diversity so not including any personal information would not help with that goal. Maybe you can just apply to the least diverse colleges you can find and that will satisfy you as being the most fair. The Ivy League has moved more away from legacies than in the past, which would seem to make admission more fair, not less. There have always been some exceptional Ivy League grads (and drop-outs) and some who were mediocre.
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