I'm with Vin Man. The tile will outlast the vanity and good luck replacing cabinets that fit exactly the same. Also staining and finishing molding to match these prefinished vanitys is a real pain to me compared to shimming but that is your choice. As far as vinyl tiles under the carpet, I'd consider removing just the loose ones and tile over them but that is your choice and depends upon if you want to deal with their extra height. Good luck.