I’m not sure if I’m understanding the request correctly, but, no, I don’t believe we have plans to add a primitive SubD box that has all edges creased.
You don’t need to insert and/or tighten edges - you can use the Crease command.
Hi @emile_francois
To add to what @wim wrote, you can just hit the Tab (or use the command SubDDisplayToggle) key to go into “flat mode”, viewing the non-smoothed version of your sub-d. When it’s time to export, you can use ExtractControlPolygon to get the “boxy” version as a mesh.