Hi @felix_fedi,
Welcome to the complex world of hex-meshing. If it's solid all the way through, then that is just a geometry restriction. A hexahedral element cannot physically connect all of those different "sides" together, because a square has 4 sides, not like 12 or so shown here. Alternatively, you can create a mesh at the top circle and drag it down through the shape, which will eliminate this issue.
@felix_fedi Actually just figured it out. You need to use SolidM (3rd button from the top under Mesh). Then you need to select your Volume to mesh (needs to be a solid) and select the Target Surface, meaning the end of the drag so your bottom or top depending on which you want to start from. Then you can either just go from there are select your element size or you can use a 2D mesh as the guide of where to start the solid mesh from, where you would click Mesh on Sources and select the 2D mesh. You can make the 2D mesh in AutoMesh.
Again, this won't be perfect since it's PrePost, but you should be able to get something reasonable.