Why does the Google Analytics module restrict uid?
There is nothing specific in the GA documentation that forbids it. There is actually a section in the GA Help which explains how to use user ids: Benefits of using the User ID feature, so using user ids is not forbidden by GA at all.

Why it doesn't work in the GA Drupal module is because of this paragraph, as stated by one of its developers (found here):


  If you upload any data that allows Google to personally identify an individual, your Google Analytics account can be terminated, and you may lose your Google Analytics data.