I agree - it's a big design error not to be able to import existing websites. It strikes me as odd, but I find it is common, at least in all of the free web design tools I have seen. I wonder if it's a cost thing? I I know that in something like IBM's Rational Application Developer, it has been possible since the product's release in 1999. Not sure about Dreamweaver.
In any case, it is a simple process. Traditionally you would download your site using FTP (Filezilla), and then work on files individually, "publishing" them using ftp again. But how strangely primitive for these times, when web design is done by Junior High kids!
Even if Google modified each web page it imported, with the "generated by GWD", it would be preferable.
Bottom line: in the year 2016, it should be SIMPLE to push a button and import an existing website into even the most basic web development tool. GWD is disappointing.