I don't understand why they don't make such an upper stage. It would allow them to refine the booster design and catch logistics while also launching payloads.
They are making an upper stage with no fins or heat shield. It's called HLS. But they don't need it just to launch payloads to orbit. Starship has such a bonkers huge payload capacity already that it's plenty for now. Nobody is asking for more yet. Testing Starship reentry is super important too, so it makes sense to do it on every launch until it's perfected.
My guess would be that it would take too much extra design work. Making the current upper stage reusable is necessary for the HLS contract anyways, and they've got a lot of work to do already on refining the heat shield & fin protection, enabling landing, and working on propellant transfer.