True, there are quite a few similar services but not many seem to work well. Our service provides better summarization (at least for the articles I tested), had additional features like extracting author name, publish data, important keywords etc and also comes with browsers extensions so you could summarize pages at the click of a button.

The method you described is a part of our algorithms but more steps are needed to make it give meaningful results and make sure it works on different kinds of articles.