How can teachers possibly do all those K-2 assessments and still teach the Standard Course of Study?

They can't and shouldn't try if they want to remain sane. What they need to do is produce a pacing guide to map out which objectives will be taught when, and when assessment of those objectives is appropriate. Then they can consult the wealth of materials presented for assessment and choose those parts that meet their needs. This on-going assessment needs to be documented and at the conclusion of the academic year a summative assessment needs to be administered and shared with each student's next-year's teacher.