The problem with Common Core, in my experience, has not been the math itself. It's the textbooks. The workbooks. The stubborn teachers.

Math is math. Knowing more than one way to solve 345 * 14 is a valuable skill. I would rather my children learn it on a whiteboard than from a workbook, and I think generally the quality of the modern texts is very poor for actually teaching math.

I also think the teachers are bemoaning the Common Core much more than they need to. Explicitly teaching the algorithms for mental math is important. Learning how to do the lattice method, even if it's not the preferred method for multiplication, is important. I've talked to far too many teachers who have complained unendlingly about the weakness of the standard, and all that the kids are being forced to learn. It feels very much like a "This is change and change is bad." mentality.

Disclaimer: I haven't encountered the Common Core as a parent at a high school level yet.