Create a profile as admin makes the admin to the Owner

I'm not sure if you are referring to an admin creating a profile in the UI, or creating a user in the UI. I'm referring to creating a user.

Creating a user as an admin has the effect that the newly created profile is not marked as default because the admin is the owner and thus \Drupal\profile\Entity\Profile::preSave thinks that a profile already exists. This is the code that leads to a wrong value of default - https://git.drupalcode.org/project/profile/-/blob/8.x-1.x/src/Entity/Pro...

An admin creating a profile OR when the create process includes creating the profiles as well.