That would be mostly redundant as the user's machine will do a lot of internal caching.
Re: the root comment of this thread, it's usually optimal to use your ISP's DNS resolvers as they're right there on your same ISP network which means your requests don't have to go out to the broader internet and are thus faster (99% of the time anyway if the hostname requested is cached on those resolvers). Using a more external resolver like Google or what-have-you means your requests have to leave your local network, leave the ISP network, and travel some distance across the internet to wherever that resolver resides.
Edit: IP anycast can allow for many resolvers to respond to one IP (such as 8.8.8.8) so it's not as if the request will have to travel the world to get an answer, but it's still generally faster to key off a resolver you know is within your same ISP.