Any small business has to manage which risks it accepts. OP got the Digital Ocean service to try and mitigate this risk to a degree. Beyond that, it becomes a question of accept risk in other aspects of product or a risk that your primary DNS server provider will fail?

The reality is, you have limited development and financial resources so you simple can’t do everything. Sure, in a vacuum, or in a larger enterprise, we’d love to manage every risk. But when we're just starting out that’s not realistic, and we do have a right to be upset at Digital Ocean's service going down while at the same time realizing that yes, ideally we would / should have had redundancy in place already.

Your question on blaming the devops team is exactly the mindset of someone who has a lot more resources than a brand new startup. In a brand new startup there IS NO devops team. If you're lucky, there is one person who does the devops work part time, balanced with a bunch of other development work he/she also does.

We have auto failover for server, app, and database failures -- this can be easily managed. DNS Nameserver failover should have been built-in, after all there is a reason we specify 3 DNS nameservers into the domain configuration, since Digital Ocean took on this task (whereby we used Gandi's DNS before that) we expected it to perform as advertised -- so yes blame lies with DO.