While you cant disable stories, please share your thoughts by using the 'Send Feedback' option to help us prioritize feature requests: https://goo.gl/WdI0BK . While every individual report may not get a direct response, we do review all the feedback sent in to us.
Get no use from features like this, clutters up the feed. A shame we cant disable it, if stories were shown on the channels profile that would be fine, but shoving it down our throats on the main page is not good design.