While I agree with not locking yourself into one company for a lot of services, I'm not sure that using a third party DNS server puts you in a better position. The Namecheap servers were knocked offline by a DDoS attack. Do you believe that third party DNS servers are more resilient to that type of attack? At least with a registrar provided DNS server, you're a paying customer and so you can probably expect some form of customer service that you might not get with a free offering.

CloudFlare is probably better set up to deal with that kind of attack because they have a paying customer base and specialise in resilient website operation, but whoever you're with, if a DDoS is big enough it'll be hard to protect against.