The CCSS is absolutely tied to testing. It's a talking point to say that the two are separate. Reformers are trying to distance themselves from PARCC because the test is so flawed and the over testing is causing national protests.

The testing has become ridiculously burdensome (and outrageously expensive). Here is an example of why it is a problem:
Right now high school kids are enrolled in AP classes. These classes are accelerated and move quickly. The AP exams are in April. The testing will be going on in March and April. The teachers won't be able to instruct the students during testing so the students have to teach themselves at home in order to be prepared for the AP exams. They also have other homework and extracurriculars.

The CCSS are now more involved (and require different methodology) so teachers take longer to meet the minimum standards. This slows the pace not just day to day but year to year. Parents have to be really savy to know how to work the system to keep their children accelerated. It can be done, but it's exhausting. This is why it hurts bright students. It's definitely a top down approach to close the achievement gap.