You don't *have* to be excited by web services, but it seems cool because it's a useful standard that abstracts away a lot of messy details that it would be easier not knowing. You can easily create an application with functions, that people running different platforms and programming in different languages can call over the web. As long as their environment supports SOAP, you can communicate, never mind all the details of encoding the data, standardizing data types, error handling, etc.
If I understand your question, SOAP isn't meant to replace using a webserver and LWP. LWP is basically a programmatic web browser. SOAP is a way of creating a web service, i.e. application that is available through the web.
Personally I haven't written a web service yet, but I've used a couple and it was very easy to do.