Null is not the problem there, null is the symptom. You see exactly the same problem if the val is a primitive type (which can't ever be null): if you access an Int from a mixed-in trait in an earlier constructor, that Int will be 0. This is a real issue, and one where I think Java has actually made the better design choice (interfaces may contain method implementations and constants but not fields - of course they had the benefit of Scala's experience when making that decision), but it's not about null.
Scala avoids the biggest pitfall of multiple inheritance elegantly, by only allowing one parent to have a constructor; classes may only be the first parent, and traits can't have constructors that take arguments. Unfortunately this doesn't mean they don't need to be initialized; in particular, vals in a mixed-in trait will be null if you try to access them in an earlier constructor.[2] As with any null, in the worst cases you may not get an error until much later on.