Why should or shouldn't a teacher only use technology to assess student learning?
The only scenario where a teacher should stick to one just one type of teaching is whenever the teacher has just one type of student. Since there is no such thing as one type of student, then there is no reason to stick to just one intervention or strategy to teach.
Using technology only, or analog teaching only, limits the student's skills and potential abilities tremendously. As Howard Gardner demonstrated in his study of multiple intelligences (MI) (1989), there are nine strengths under which students can perform and excel academically.
Technology is only one of several teaching processes from which students can learn. Even in the digital age, there are bound to be students that may prefer to learn through manual skills such as arts and crafts, others through poetry or literature, others may even prefer to problem solve mathematically, and there is always the odd percent of students who suffer from "Technostress" and get frustrated too quick if the technology is too complicated, or not fast enough for their taste.
The intelligences are:
Linguistic intelligence- capacity to understand and produce language, both natural and acquired through 2nd language. Entails appreciating patterns, trends, sounds, and semantics. Often this type of student tends to look for similarities instead of differences.
Logical-mathematical intelligence -capacity to reason deductively, problem-solve, self-pace, use common sense, and think both inductive and deductively.
Musical intelligence -appreciates patterns, trends, rythm, decoding, and connecting; similar to linguistic and mathematical intelligence.
Bodily-kinesthetic intelligence - using the body to problem solve
Spatial intelligence -understanding patterns, compartmentalization, and spacing
Interpersonal intelligence - understanding others (socially)
Intrapersonal intelligence - understanding oneself
Hence, in Howard Gardner's own words:
..seven kinds of intelligence [9, minus naturalistic and spiritual intelligence] would allow seven ways to teach, rather than one. And powerful constraints that exist in the mind can be mobilized to introduce a particular concept (or whole system of thinking) in a way that children are most likely to learn it and least likely to distort it.
Therefore, it is best to apply the MI model in the classroom so that teachers can tap on every possible chance for a student to succeed. Included is an Enotes link to Gardner's excellent book on teaching styles titled The Unschooled Mind: how Children Think and How Schools Should Teach (1991).
This answer is long after your question and the excellent answer you received above. I just have one thing to add which I think is critical to the success of students who are being assessed. Just as the new GED tests are going to be done only with technology using computers, I see a huge problem. Many students are going to be tested with a significant disadvantage as their computer skills will be tested as much as their knowledge. Too often people believe that everyone has access to computers and the skills among students are equal. That is a false assumption and when a test is timed, the student with the least familiarity with computers will be at a distinct disadvantage. This is especially true when it comes to written essays which are now supposed to be graded by computer also to make the grades less subjective. I just see too many students, whether adults trying to do a GED program to better their lives or younger students trying to pass state mandated tests, with discrepancies in their abilities to utilize the full potential of a computer to enhance their product of assessment.