> Since there was and remains no algorithmic method of finding the highest level at which a domain may be registered for a particular top-level domain
A centralized list like this not just for domains as a whole (e.g. co.uk) but also specific sites (e.g. s3-object-lambda.eu-west-1.amazonaws.com) is both kind of crazy in that the list will bloat a lot over the years, as well as a security risk for any platform that needs this functionality but would prefer not to leak any details publicly.
We already have the concept of a .well-known directory that you can use, when talking to a specific site. Similarly, we know how you can nest subdomains, like c.b.a.x, and it's more or less certain that you can't create a subdomain b without the involvement of a, so it should be possible to walk the chain.
Example:
c --> https://b.a.x/.well-known/public-suffix
b --> https://a.x/.well-known/public-suffix
a --> https://x/.well-known/public-suffix
Maybe ship the domains with the browsers and such and leave generic sites like AWS or whatever to describe things themselves. Hell, maybe that could also have been a TXT record in DNS as well.