Get author meta of all writers

Not exactly sure what you’re aiming at with your queation, because, why shouldn’t it be legit to get the data you want by looping trough the available users, to be exact in one way or another you kind of have to do it this way, get the users and then get the user meta to display – so I’d say, it’s legit.

Concerning your approach there is to note that get_the_author_meta() doesn’t take user objects, it expects the user ID, so you either have to make use of the fields parameter of get_users() by specifying it to return an array of IDs. Like this:

$admins = get_users('role=administrator&fields=ID');

Or you specify the fields parameter to return user objects that already include the user meta. Like this:

$admins = get_users('role=administrator&fields=all_with_meta');

If you’re going to use the latter option you have to change your the_author_box() function accordingly.