Is there a technical reason why mesh generation is restricted to tetrahedral shapes? Having the option to:
1) Apply a quadrilateral mesh in at least one direction (quadrilateral pyramid or triangular prism) or a full hexahedron mesh, and
2) Align the mesh orientation to an edge or set of edges,
could help with computation time and accuracy depending on the boundary conditions.
You introduce biases with any mesh, but its generally better to simulate certain shapes like a rectangular sheet with quadrilateral elements instead of resorting to smaller element sizes to resolve some geometry.