How obtain the uid of the logged user as a related field in a view?
You can't without some custom module providing such a data field (such as views php as you've seen).

Unless the uid has some relations to the content type you're displaying (e.g. a user reference field, the node uid, etc.), there's no way to retrieve the current UID. Views is designed to pull in data from a base table (e.g. nodes, users, taxonomy, etc.) and display the fields directly attached to it or related to it through a relationship.