I'm not normally a big reader of short stories either. That's exactly why I did set a target of one a day.
Otherwise I never read them. I've just finished Gene Wolfe's Book of Days, an ex-library paperback I've owned for at least 15 years and hadn't opened until this month.
It's great if you can make the time. You constantly get extra "free" books read in addition to your regular novel-reading. The main problem I have is finding stories of the right length. Modern shorts can be pretty long. Ideally I want something that will take less than half an hour to read. I'm not sure any of the stories in Dangerous Women by George RR Martin and Gardner Dozois has been that short, so I haven't got far on that one.