Movements in the substrate can cause cracks to form in your new tiled surface. Old or damaged substrates, such as wooden floors can be particularly prone to this problem. The installation of anti-crack matting, or decoupling membrane as it is also known as, ensures small cracks in the substrate are absorbed by the matting, in effect the tiles are decoupled from the floor and cannot be damaged. The mats are easy to fit and provide added peace of mind for your tiling installation.
This from the internet so I guess the tiles can come up without damaging the floor (but ask your tiler). I still think hardwood flooring would be best at absorbing any movement, however it’s caused. I have laid LVT and can’t imagine it would crack like tiles.