When manually assigning a static IP to specific interfaces as per docs, it may be possible that you have to manually specify a DNS nameserver in the /etc/resolv.conf file if DHCP was not applied to an interface(s). Or, because you have not installed a network manager service like NetworkManager or ConnMan

dhcpcd(8) states very clearly that it does attempt to write directly to /etc/resolv.conf under a condition.

dhcpcd is an implementation of the DHCP client specified in RFC 2131. dhcpcd gets the host information (IP address, routes, etc) from a DHCP server and configures the network interface of the machine on which it is running. dhcpcd then runs the configuration script which writes DNS information to resolvconf(8), if available, otherwise directly to /etc/resolv.conf.

I believe it can be beneficial to add this small piece of information in the docs for users who primarily use a tethered connection with no DHCP, in order to reduce any potential future confusion on why their network utilities and software respond back with name resolution failures.