Personally, I have some scepticism about the CTM largely because it arose with the development of computers. My feeling is that the CTM is an attempt to map the phenomenology of mind onto the structures of computers. It may be that at the level of third-person experience, a computer and a person could be indistinguishable (c.f., the Turing Test) but this doesn't guarantee that the two have the same internal mechanisms.
However, it may be the case that with the advent of computers, we have learned a new way to look at the world and this actually explains how the mind functions. But I doubt it.