Earlier quoted context omitted.
You could also do an in-between step of host -t soa example.com which should give you domains that have any DNS record at all, not just an A record.
Is there still a point talking to the registrar then? How common is it for a domain to exist with the registrar but have no SOA record?
If the registrant creates any DNS records at all, then the SOA will need to exist for the zone to be valid; but I don't recall whether the registrar is or isn't required to publish a zone for a registered domain that otherwise contains no records. (Also whether the registrar is required to inform the registry of authoritative nameservers for the domain at all times from the moment that the domain is registered, and then whether that information would lead to the synthesis of a SOA record.)
I guess I can either try this (if I could find a no-frills-enough registrar that doesn't create any records at all for add-on hosting services or domain parking) or try to take some more ICANN coursework to find out the answer.
Or maybe someone else reading this thread knows whether we can have a domain in practice that is registered but has no published SOA.