I like the idea of using a limited vocabulary, not as a tool to write scientific papers, poetry, or novels, but to teach clarity. Write with this app for 15 minutes every day and your writing will likely improve. It’s a lot like practicing scales on a musical instrument. Scales reduce the complexity of practice to pitch and tone so they can be addressed individually. They are essential in developing a sound instrumental technique but not sufficient. I believe this is a valid analogy to writing with a limited vocabulary.
The problem is that by being restricted to a limited vocabulary people in practice would find it necessary to assign additional meanings to existing words in order to express meanings outside the ordinary lexicographic meanings. Listeners would increasingly be required to ascertain meanings by context. This is easy for humans; we do this many times a day without effort, or even consciously. Our brains are particularly well-fitted to accomplish this complicated task.
That is why Newspeak would be almost impossible to implement. Preventing people from inventing new meanings for existing words is simply impossible.
The problem with a rigid vocabulary is that the natural process of assigning new meanings to words would begin to overload existing words. This increases the danger of ascertaining the intended meaning of a word when it can mean a number of different things, not to mention the difficulty a stranger to the context would experience in interpreting what is being said.
Thus the case for a larger vocabulary rests on the need for greater precision. A thousand words isn’t enough, just like the mastery of scales does not by itself define, for instance, a violin virtuoso. Too many words, however, is not so formidable a problem as too few, because human beings generally develop a vocabulary that they need, depending—once again—on context.