“When I told him that this was an email that was no longer available to me, and that it hadn’t been my email of record with GoDaddy for more than 20 years, he said he could change the address, but that would require me to activate two-factor authentication, and that there would then be a 24-hour delay before he could make the required changes.”

Sounds more like a security issue honestly. Not sure you would want them to simply take your new email as trustworthy