For the most part, having legs or a box isn't very different. I know someone who has cabinets with legs, and they sell toe kicks that attach to the front, so it looks just like a cabinet on a box (like this https://www.canarycabinets.com/dsc03526/). However, as @grue pointed out, it's not clear to me how you'd secure an island cabinet with legs. For boxes, you attach a board to the floor, then attach the box to the board (see Figure 13 here https://www.familyhandyman.com/list/how-to-install-cabinets/). What keeps the island you have secured? If it's only attached at the wall, I would think it could flex if force is applied to the end far from the wall. Does something hold it to the floor?