If you register a domain with Cloudflare or Route 53, and that service goes down, do your records stay active in the DNS servers? What if the DNS servers go down, I know a lot of people use 8.8.8.8, so if Google’s server goes down, then DNS fails?
What are the potential point of failures for having your own domain?
Correct, but not the whole story.
If your registrar goes down, and you have your authoritative DNS anywhere else, then literally nothing happens. They just register the domain for you and give you an interface to pass your ‘glue’ records up to the TLD root servers.
If those glue records point to on-site DNS, or anything that is not your registrar’s DNS servers, then your registrar being down is inconsequential other than that you would not be able to update your glue records, or renew your domain.
A separate question of “what happens if my authoritative servers go down”, is answered above.
The two are not one in the same, though they can be.