It's lkely TPS (thermal protection system) concerns pushing them to stainless. They're going for a "hot frame" design, where you permit re-entry heat to enter the superstructure. The Shuttle (and all capsules) have a "cold frame" that is protected by a heat shield. The Shuttle airframe was lightweight aluminium that could not withstand the heat of re-entry, so the whole craft was insulated by tiles and blankets. The X-15, by comparison, had a titanium skin and airframe. The heat of hypersonic flight was absorbed into it, while just the pilot's cabin was insulated.
Starship will do the same, and will also have elements of active cooling, whereby the cryogenic fuel needed for landing is pumped through the windward skin during peak re-entry, in much the same way that the engines are cooled during a burn. In addition, the shiny steel will reflect much of the radiated heat from the bow shock plasma. The crew/cargo compartment at the top will be insulated against the hot spacecraft.
This is a "heavy" solution when considering TPS on its own, but it looks like (carbon fiber + TPS attachment + TPS + metal parts required for strength in the fins/airbrakes) was going to weigh the same as a stainless steel frame that did everything.
This hopper though, is just being made shiny to look cool.