Why doesn't morphing fix haircuts, then? Why doesn't morphing eliminate scars (we've read about scarred Andalites)?
My theory is that morphing takes into account your mental image of yourself. It'd have to, because there are loads of things about your appearance that aren't determined by DNA alone. Weight, for example, and even height, have to do with how healthy/malnourished you are, and that isn't written into your DNA.
Thus, certain things about yourself (height, weight, haircuts, piercings, scars) are taken from your subconscious mind, rather than your DNA. And since it's your subconscious mind that determines it, you can't alter your appearance consciously (Rachel complains about not being able to fix a bad haircut by morphing, at one point).
So there you go. The morphing technology is thought-controlled in more ways than one.