Which gap do you mean?
I think @grue is referring to the gap between the floor and base of the cabinets. In the US, it is nearly ubiquitous for cabinets to sit on a box, and the front edge of that has a toe kick, like shown here: https://www.thehandymansdaughter.com/wp-content/uploads/2021/10/toe-kick-with-mitered-outside-corner-960x960.jpg.
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?
I have an attic that gets direct sun until the afternoon. It gets quite hot. I had easy access to the rafters so I used radiant barrier, and the difference is very big. As you’re putting it up you can tell that it’s blocking the heat standing in an a covered vs uncovered area. In subsequent days when it was all up it was obviously cooler. It’s still hot but not unbearable.
Radiant barrier is more expensive and fiberglass probably would have worked just as well in this situation, but I didn’t know enough about air flow in that space to tell whether fiberglass would impede anything,so I used radiant barrier and left a gap at the bottoms and tops. It is very easy to install. Fiberglass wouldn’t be too hard either, but the barrier is daed simple and there’s less volume to move around.
In general, my experience say it’s going to help, and whether you do fiberglass or radiant barrier is up to you.