They are useful not only in conjunction with infinite data structures. Take my example state transformer "everything" and modify it so that it calls next exactly two times, not infinitely many times, and outputs a pair of the outputs of the two next invocations.
Now let's assume you use this pair in a context where only its first component is used. Without lazy patterns, next would be invoked two times although it need to be invoked only one time. So you might have unnecessary evaluation. And you might have something even worse. Let's assume that when we apply the function making up next on the output state of the first next invocation then we get _|_. Without lazy patterns, just using the output of the first next invocation would result in your program aborting. Of course, it shouldn't do so.
This is a good example! But now I got the impression that pattern match failure could happen in many places, so unless you want it to fail loudly, you shall always use lazy pattern? Thanks, Fan