Because most guides are written for people who are not experienced and it is assumed to be safer (by reducing possibilities for mistake) to prevent the private keys from being transmitted/stored outside of the client on which they were generated.
ssh-keygen command also automatically sets the limited permissions to the generated private key reducing the number of steps required.
Where you generate the keys and how you distribute them depends solely on the process (in the "management process"-sense). As long as you do not the compromise security by using an insecure generator or an insecure channel, the exact place where you generate the key pair does not matter. It might as well be a third machine.