I always thought that if your muscles were rotting, and you were no longer smart enough to be able to use the most basic of tools, you shouldn't be that much of a threat on your own. The threat in classic zombie films comes from being alone and being outnumbered 10,000 to 1 ...
Beyond that, the reason Dawn of the Dead was considered a classic is because of the statements being made by the movie. While it doesn't seem that original or outrageous today, a lot of the movie was a statement on out of control consumerism in America which was pretty revolutionary in the 1970s.
Edit: I should also say that I am a pretty big fan of classic zombie films, and loved renting them long before there was the Zombie resurgence that happened in the past decade or so. They are often fairly cheesy, poorly acted and written, and are generally very bad movies by most measures but they are far more experimental and have a more interesting "Style" than is presented by most modern movies.
