Yes, they did. But, depending on the details of the attack, I am not sure if any other provider could have withstood the attack without problems. In other words, I doubt there's a single provider/alternative.
Unless you have a good argument why they are less likely to stay up than the alternatives, I don't see how this would lead to their end. Unless you take it as an argument to abolish ALL DNS servers and start mailing host-files around...
People have been painfully reminded why using multiple providers is best practice, will re-evaluate if that's worth the expense and if yes add other servers. Dyn will easily survive unless some massive blunder is exposed in the aftermath.
Would anyone else have stayed up, though? This isn't just going to be a fear response, the risk assessment will be to ask "what could have prevented this?"
Lots of people will quit using Dyn as a sole DNS, but I don't see any reason they'll quit being involved in people's multiple DNS solutions.