When I think of "offering a domain", I immediately think of DNS subdomain delegation. And on the linked page, you do say "DNS alteration encourage", which could suggest that subdomain delegation is what you had in mind.

But the rest of the text suggests more than subdomain delegation? How do you envision that self-hosted services might operate underneath the "top level" domain if not by delegation? Do you mean that an API would not create a delegation but would simply create a single record?

To be clear, a delegation of "xyz" under example.org would mean that some other DNS server is now authoritative for the entire *.xyz.example.org tree in DNS. That allows the delegate to create their own records for foobar.xyz.example.org or mail.xyz.example.org. Whereas if there was just a single AAAA record named "xyz" under the example.org domain, then the only name that will resolve is xyz.example.org; there is no additional authority to create subdomains under xyz.example.org.

In either case (a delegation or single records), you could certainly develop an API or some sort of Git repo as the source that is referenced by the top level domain's nameserver. This is quite similar to how DDNS providers work. And a while ago, someone on Mastodon (I think) used a custom nameserver to send football/soccer scores via DNS lookups. Or tunneling IP itself over DNS.

In the non-delegation case, some services might need more than one record created. For example, a simple web server at the xyz.example.org subdomain needs at least two fecords (A and AAAA) to support both Legacy IPv4 and modern IPv6 clients. If doing an email server, it would need at least an MX record, but modern DKIM and SPF might require additional TXT records and maybe SRV records.