The issue of accuracy aside, my main objection to teaching someone how to cut using the lines is one of fundamentals.
If you are in a situation where you don't have a mat with lines
(workshop, class, retreat, at a friend's, etc.) can you cut without the lines? I have a friend who can't, and sometimes it's a problem when we get together and she has to use a mat without lines...she just can't do it. But then, I'm a dinosaur and I think beginners should at least have a rudimentary knowledge of drafting patterns and making templates. Okay, you can get your guns out to shoot me...