Hi Karen, did you find anyone who can give you some advice on concrete countertops? I love the look, and do not believe you need to place it over an existing countertop if you don't want to. I found an ideabook written by a Houzz writer about countertops made with concrete, which hopefully is a little helpful: https://www.houzz.com/magazine/amazing-ways-with-concrete-countertops-stsetivw-vs~294898

The application of concrete over existing countertops is actually a thin cementious overlay applied to the counters. The original counters have to be structurally sound and stable. The material is applied and troweled to a finish ranging from textures to glass smooth. Colors can be added to mixture and stain can be applied to product when dry to achieve multiple looks. True concrete countertops are solid 1-1/2" thick typically to match exisitng standard countertop depths. These can be applied on site but most are precast by concrete artisans in a controlled environment shop. The colors, shapes, techniques are nearly endless given concrete fluidity when casting. If you have any questions feel free to check out my home page and ask. Hope this helps. If you decide concrete is for you, find a local artisan to meet with and design the counters.