Some commercially available systems support such meshes. Unfortunately, the computational geometry of hexahedral mesh generation is so little understood that existing systems suffer major drawbacks. Unfortunately, many starting configurations are unfillable. Conversely, the inside-out approach fills volume and produces boundary meshes as a side effect. This has the disadvantage of leaving us no choice in the boundary meshing.
Intermediate strategies are yet to be investigated.
Some tetrahedral mesh generators use the advancing-front approach as well. These generators typically place Steiner points in successive layers and then use the Delaunay triangulation as the mesh. Uniting mesh generation with CAD systems is much needed. The idea is to produce grids directly from the CAD geometry and at the same time retain independence of grid characteristics. Not only would this solve a compatibility issue, but it should also make the mesh generation task easier.