Just for the uninitiated:
suid binaries are binaries with a special flag set that will make it run with root privileges regardless of who started it.
sudo is an example of something that would use suid. When a user runs sudo, the binary actually runs with root privileges from the get-go, checks if the user is OK, then executes the command you specified.
However, use of sudo or other suid binaries is entirely pointless in an alpine container. There being no password also does not matter, as you are by default already running everything as root. Who cares if root can become root?