I would certainly not quibble with your interpretation of the "do" operator as an important "standard" way of describing certain important kinds of intervention, and there is no doubt that its semantics and application deserve very careful consideration.

Now it may or may not be the case that many (if not all) of the various manipulations can be reduced to "do". What certainly is the case is that all applications of "do" are special forms of a more general manipulation operation. If we want a broad and fundamental theory of causal inference, it seems to me inappropriate to base it on a special case, no matter how important that might be. The language of decision trees, influence diagrams, conditional independence manipulations of intervention variables, etc., is perfect for describing and manipulating the requisite degree of additional generality, and, very importantly, by allowing us to express explicitly what we mean when we specialize it to the kind of problems covered by your interpretation of "do," allows us to speak clearly and without fear of misunderstanding. Rules such as those in the Theorem 3.4.1 of your book, while perfectly valid (and readily derivable through influence diagrams) in such special cases, do not appear to me to be sufficiently fundamental to form the basis of a "calculus".

Author's reply
I was about to elaborate on how science thrives on reductions to basic concepts, how science chooses its basic concepts, why the chosen concepts are necessarily "special cases", and why it is inevitable, therefore, that "broad and fundamental" theories be based on "special cases" (see my reply to Bill Shipley). But then it occurred to me that the (almost perfect) analogy with chemistry would be instructive at this point, and that the following hypothetical letter would convey the message better than any philosophical discussion. Here is a letter that could have been received by John Dalton from one of the many contemporary critics of his atomic theory of matter.