For Vote-By-Mail to be considered and legitimate, the States would need to verify their voter registration rolls are up to date and clean in accordance with federal voting laws.
Title 52 USC Chapter 205 National Voter Registration
52 USC 20506: Voter registration agencies
https://uscode.house.gov/view.xhtml?req=granuleid:USC-prelim-title52-section20506&num=0&edition=prelim
52 USC 20507: Requirements with respect to administration of voter registration
https://uscode.house.gov/view.xhtml?req=granuleid:USC-prelim-title52-section20507&num=0&edition=prelim
(this federal law provides requirements for up to date voter registration rolls)
US Code Table of Contents link:
https://uscode.house.gov/browse/prelim@title52&edition=prelim
Sec 20505, 20506, 20507 pdf included