“Don’t mesh it” is not an option. “Solid geometry” concept only exists in CAD software - it refers to parametric representation of a shape, obtained from combining simple parametric primitives and can be characterized with a few hundred or maybe a few thousand parameters. In contrast, in medical image computing you generate shapes from images, which consists of tens or hundreds of millions of voxels, so the resulting object cannot be practically stored with a parametric representation (you would need thousands of times faster CPU and thousands of times more RAM).
Image segmentation results therefore typically stored either as a 3D array of voxels or as a polygonal mesh. In rare cases, when the shape is very simple, you can reverse-engineer a parametric shape (“solid geometry”) from the segmented shape in your CAD software, but in general you need to use different tools to deal with these complex free-form shapes. For example, for finite-element analysis you generate a volumetric mesh; for Boolean operations, you need to use special algorithms that work on polygonal meshes (or use voxel array representation); …