My kids are in school doing common core and that's not what it's like at all. They do worksheets around learning specific small-bore topics, but otherwise do a ton of book reading and long-form writing assignments. Unless you have a cite, I don't think you're representing what the people in this article are talking about.
I wasn't addressing the article, just the GP. My experience was with my daughter's school. She was in 1st grade five years ago, but through 4th grade she was still bringing home piles of worksheets that had been done in class, and some more for homework(!). Talking with other parents at other schools at the time, they had similar experiences. I'd be thrilled if five years has made a huge difference, but I'm not optimistic.
I should note that we're in a not-terrific school district, and that there's a whole chain of people from the teacher up to state legislators on up to, I suppose, Betsy DeVos who can effect how the standards are addressed.
More anecdata: my younger two are bilingual and didn't know how to read more than really basic sight words before starting K (common core class). They are now highly proficient at reading (english), which (they are decent learners and have no challenges) I reason are due to two things: 1) An interest in reading which is fostered by the class atmosphere - they have "choice" time and some of that can be reading. 2) They have an expectation in class to spend a lot of time reading or being read-to.
I will admit we did read to them every night since they were babies, so that's probably also helpful. But kids usually love the bedtime story.