This is what C# program manager has to say:
Why doesn't C# have a 'with' statement?
Small or non-existent readability benefits. We thought the readability benefits were small or non-existent. I won't go as far as to say that the with statement makes code less readable, but some people probably would.
Increased language complexity. Adding a with statement would make the language more complex. For example, VB had to add new language syntax to address the potential ambiguity between a local variable (Text) and a property on the "with" target (.Text). Other ways of solving this problem also introduce language complexity. Another approach is to push a scope and make the property hide the local variable, but then there's no way to refer to the local without adding some escape syntax.
C++ heritage. C++ has never had a with statement, and the lack of such a statement is not generally thought to be a problem by C++ developers. Also, we didn't feel that other changes -- changes in the kind of code people are writing, changes in the platform, other changes in the language, etc. -- made with statements more necessary.