Lets see: The Public school system has unlimited funding via tax payer dollars. So yes, they can afford to accept a child with no thoughts about the cost involved. Private schools (Jewish/Christian/Islamic/Non- religious) aren’t funded by the tax payers and thus have a limited budget and at the end of the day have to meet payroll, pay the bills and all other expenses that come with running a school. Your comparison between Yeshiva administrators and Public School administrators is (not surprisingly) appalling and dishonest.
As an aside, many illegal immigrants (estimated by Congressional Budget Office at 50-75%) pay Federal/State/local taxes, and all of them pay taxes like sales tax. I’m not saying the taxes they pay into the system offsets what they take out, but saying they “pay zip” isn’t completely true either.