That's a very profound question.
IMHO
Printing is the process of reproducing an original image multiple times. As such it should be a faithful reproduction of the original and should not introduce any elements that are not part of the original.
Halftone screening in offset (and flexo) is a method to convert an analogue/continuous tone original into the binary format needed for a press.
So, the halftone screening method should, as much as possible, be a faithful reproduction of the original and should not introduce any elements that are not part of the original. IMHO FM type screening does this better than AM and is one reason I prefer FM over AM (there are other benefits to FM but that that's a different topic).
When it comes to AM and derivatives like hybrid AM/XM a similar rule applies and you have to look at the subtle details.
For example, in a classic AM screen (Euclidean round/square/inverted round) there is an optical bump at the 50% tone. So you would look at how the screen deals with that artifact to minimize its visibility. Or you could look at rosette drift from clear to dot centered over the diagonal distance of a plate ( rosette drift causes tone and color shifts). I could write a book on the topic LOL This blog post will give you some of the basics:
http://the-print-guide.blogspot.ca/2009/02/am-screening-halftone-dot-shapes.html but, of course, one can go much deeper into the subtle details.