there is a separation inbetween public and admin.
is there any other reason, than one should be publicly accessible and the other not?
I am not sure what you are asking here, sorry.
The admin should be able to have control over the system and public users should not be able to control the system.
Admin Endpoints are privileged endpoints typically exposed to your internal network and never exposed to the public internet without access control.
Public endpoints can be exposed as is to the outside world.
More information. https://www.ory.sh/hydra/docs/production