A web site needs to take into account much more factors than the actual web pages themselves. You need to think about information architecture, conversion rates, search engine optimisation, download times, server loads and more. You don't need to have source code level knowledge of your pages for all of these elements, but it is a must for some of them. Without understanding the source code, you won't be able to develop a thorough understanding of server load, download times and most important, some aspects of search engine optimisation.
When you code a page by hand, it makes you look at the page structure and really understand where your elements are. This is very important with today's search engine technology. Search engines see your website in a manner that resembles the source code much more than it resembles the output that the users see. This is a great example as to why we need to have a close handle on what the source code looks like just as much as what the browser output looks like.
So if you're interested in making a web page that looks nice, there really isn't any reason not to use Dreamweaver. But if you're looking to construct a complete website that's going to involve all of the elements successful sites require, you're going to need a better understanding and better control of the source code that drives each page. Even if you're only interested in making a page that looks nice, you really should consider the benefits of hand coding it or at least thoroughly understanding the code that Dreamweaver generates.