Most recursive resolvers try to figure out which authoritative server for a domain responds fastest and use that one. If you've got enough DNS requests and enough DNS servers, it kind of works out ok without anycast. Although, I've been told that 4 authoritatives is the optimal number, which is limiting (you can do more of course, but a random internet use recalls but can't find a writeup suggesting more wasn't great in some semi-failure cases, and you can cargocult top X domains which seem to do 4 for the most part)

Advanced protocols may be able to use SRV records to distribute further traffic, but web browsers can't, so kind of stuck for them.