I do not believe the politicians or the media are speaking at all about the total cost a school voucher recipient pays. Political statements are a bait and switch ploy.
A voucher applicant succeeds in the voucher lottery – asserted to be valued at about $4,200. The recipient then presents voucher at private school but is told that the tuition will be several thousand dollars more, to be paid out of their own pocket. In what way does this benefit a lower-income family? They did not have enough income to go around before the voucher.
In what way does it help a higher-income family? Very practically with a public subsidy cutting the private tuition they were prepared to pay anyway! Now there’s an offer one does not turn down.