It's like not testing if your calculate application can handle negative numbers or decimals.
Similarly, what about tags (https://en.wikipedia.org/wiki/Tags_(Unicode_block) )? Do these require an U+E007F CANCEL TAG?
The 66 noncharacters certainly need consideration. http://www.unicode.org/faq/private_use.html says:
“Because of this complicated history and confusing changes of wording in the standard over the years regarding what are now known as noncharacters, there is still considerable disagreement about their use and whether they should be considered "illegal" or "invalid" in various contexts”
Edit: also, testing all code points likely is overkill and using code points in isolation likely isn’t enough. Most tests are better of with something like the big list of naughty strings (https://github.com/minimaxir/big-list-of-naughty-strings)