Unfortunately the public suffix list has serious security implications, so it isn't safe to distribute it via unauthenticated DNS.
It also has very serious availability implications, so if you sign it with the WebPKI-maximum validity of 90 days and somehow and those signatures expire, you either get major vulnerabilities if you fail open or else an entire TLD (like ".com") breaks if you fail closed. You get to play this game every 90 days. Sounds like fun. https://www.digicert.com/blog/chromes-proposed-90-day-certif...
This is the fundamental problem with trying to have DNSSEC replace DNS (instead of augmenting it): signature revocation is Byzantine-Generals-complete, which means that you either sign something forever (like ssh keys) or for a fixed time period and treat nonrenewal as revocation. Nonrenewal-as-revocation sorta works for signing single domains; if one website's cert expires it isn't the end of the world. When you start trying to sign larger and larger fractions of the Domain Name space, moving up to ccTLDs and then the root, the stakes are just way too high.
This is why DNSSEC will never displace unauthenticated DNS.
The choices are to stick with unauthenticated DNS, or maintain both systems in parallel forever. There is no third option where unsigned DNS records just go away.