There are two latemen because of multiple edition deadlines, two wire editors and five rim editors, although the latemen and news editors will work the rim on busy nights. About half the desk is made up of career copy editors. There is no set career path, but the paper often promotes from within, and copy editors have moved into other positions. I'd say yes. People tend to get treated with the respect they deserve.
Squabbles are few and far between.
Some elite reporters get to circumvent the rim editors. This is only resented until the rim editors see the news editor poring over a 600-inch screed. A nice policy here is that all copy editors get to work the slot once they have been here a year or so and are deemed ready by the news editor. The paper has separate paginators. It has toyed with the idea of training copy editors as paginators but so far has not done so.