No, this intuition is incorrect.
By using one of UUNet's (or someone else's) public caching name servers, you're increasing the cache diversity in a very widely used public cache and reducing the overall load on the global root name servers AND domain-level authority servers by reducing cache misses and reducing query traffic in a cumulative manner.
Think about it in terms of extremes/limits. If everyone on the internet ran their own server, would the root infrastructure slow down or speed up?
Personally I think it's somewhat insane and counterproductive to setup a DNS server on your laptop - not only are you wasting your own CPU cycles, you're wasting the CPU cycles of the root name servers and CPU cycles of the domain-level authority servers. Why do that when there are numerous public cache servers setup specifically for this very purpose?!
There's a reason those massive cache servers are accessible by the public internet. They help it work.