Thanks! I'm one of the devs on the project; you can contact me directly at Zane@Streamified.com.
To your questions: one of the major benefits of the service is the "crowdsourced" aspect of it. That is: the more people using the same API, the more news articles get found and indexed. Furthermore, the API actually hooks into other paid APIs, so it actually wouldn't work very well for you to run it on your own servers unless you wanted to also pay for them. For all these reasons and more, we think that a hosted API is the best solution.
To your questions: one of the major benefits of the service is the "crowdsourced" aspect of it. That is: the more people using the same API, the more news articles get found and indexed. Furthermore, the API actually hooks into other paid APIs, so it actually wouldn't work very well for you to run it on your own servers unless you wanted to also pay for them. For all these reasons and more, we think that a hosted API is the best solution.