Using the same calender every year might work fine in America and some of the Western European countries. (According to the article, Easter and Thanksgiving can be given fixed dates in the 13-month calendar.) But many non-Western cultures have holidays tied to phases of the moon. Chinese New Year would still move around a lot from year to year, making it impossible to reuse last year's calendar. Ditto for Chuseok in Korea, which needs to coincide with a full moon.
So yeah, this looks like a nice change, but it's not going to be completely static from year to year in every culture.
Besides, I don't think it will completely eliminate the difficulty of figuring out what date "next Thursday" is. We at HN tend to be mathematically competent, so we can easily calculate multiples of 7 in our heads and subtract a few without breaking a sweat. Most ordinary people, on the other hand, have difficulty figuring out what date next Monday is even when it's Friday and you just need to add 3. They'll just look it up in a paper calendar or their mobile device.
So yeah, this looks like a nice change, but it's not going to be completely static from year to year in every culture.
Besides, I don't think it will completely eliminate the difficulty of figuring out what date "next Thursday" is. We at HN tend to be mathematically competent, so we can easily calculate multiples of 7 in our heads and subtract a few without breaking a sweat. Most ordinary people, on the other hand, have difficulty figuring out what date next Monday is even when it's Friday and you just need to add 3. They'll just look it up in a paper calendar or their mobile device.