To add to a1369209993's comment, an alternate DNS might be faster (as Cloudflare claims for 1.1.1.1), too. Or more stable than your default DNS. But for me, anyway, I made the switch after Frontier started pulling the NXDOMAIN stunt.
I'm aware of the problems with ISP-provided resolvers. I meant running your own resolver, like named, which queries the root zones itself, supports DNSSEC response authentication, etc.
In that case: local resolvers involve actually installing and configuring a recursive dns server, which isn't everyone's idea of fun, whereas 1.1/8.8.8.8 can be set up with a one line config file edit and then forgotten about.