Actually, the idea behind it being a mesh is only that the holes are smaller than the wavelength of the EM wave you're trying to block. So theoretically, a fully solid metal container will be just as good as a mesh in terms of blocking radiation. Or potentially even better, as wavelengths smaller than the diameter of the holes in the mesh you're using will still pass through, but won't pass through the solid metal container
I think the main reasons they usually go mesh vs solid are so you can see inside it (e.g. microwave, visible light wavelength is smaller than microwave wavelength so can pass through where microwaves can't, letting you see your food) and to save on costs (i.e. why use 100g of metal when you can get away with using 50g)
