Reduced Ad Blocking Capability
The main reason you should Pi-hole as your only DNS server is that you will see increased performance in the blocking of ads.
If you have two DNS servers (Pi-hole and something else), your network clients may not always query Pi-hole for name resolution. If a query happens to be answered from a non-Pi-hole DNS server, your block lists will not apply (since that DNS server doesn’t know about them).
All Queries Need To Go Through Pi-hole First
Since other DNS servers (like Google’s public ones) don’t know about your block lists, they cannot block the advertisements. Pi-hole allows you to set upstream servers for legitimate queries, but if they don’t pass through Pi-hole to begin with, the domains queried may not get blocked.
What About Redundancy?
If you have Pi-hole as your only DNS server and it fails, your network will stop working and you (technically) wouldn’t be able to browse the Web. So many people set a secondary DNS server in a fashion similar to the screenshot below.
However, the problem with this–as stated earlier–is that your network devices may use either one of the servers to get their queries answered.
It’s Not Much Of A Problem
Many existing home networks use their router as their DNS server–their only DNS server. So if your router fails, you’ll also lose access to the Internet. So the difference between using just Pi-hole or just your router’s DNS server is negligible.
Using A Secondary Pi-hole
If you were concerned about redundancy, you could always set up a secondary Pi-hole and use it as an upstream server for the first.