Ever wondered why you would want to separate your woofers and tweeters? Very simply, it just sounds so much BETTER.
Normal speakers combine the two, convenient yes but at the expense of pure audio performance. By separating the components and then bridging them with a crossover, you can ensure different frequencies go where they need to, up to your tweeters or down, to your woofers.
This means each component is doing the job it is best at, rather than an average blend that comes from a normal speaker. The result is greater clarity, distinction, balance and a better performance all round.