I have seen a chain link fence covered in mesh and stuccoed. The finish is up to the mason's skill and imagination.

Fiber cement has no elasticity, so rather than flexing in high winds it will crack.

A solution with several pieces may work for you. Identify the places where you need privacy, then the places where appearance is important (front of the house?). You might be able to use the more expensive masonry in some areas and metal fencing in other areas. Local fire and seismic codes get updated, so check with local building permit authorities (especially for height) and your insurance agent. Sometimes fence damage is covered by insurance, sometimes not.