Today we have bikes that can ride virtually any terrain, carry hundreds of pounds of cargo, soak 10" bumps at 60mph, ride backwards down vert ramps, accomodate limited-mobility riders, and access enough gears to put you in the right pedal cadence in just about any grade.
Yes, it's two wheels, pedals, and a chain. Yes, it's still the diamond-frame safety bicycle. But it has changed.
It's a market where all you can buy is the kids plastic version of a Porsche or a literal Porsche.
The real challenge of improving anything in cycling, from an industrial design perspective, is that a bike is a product whose primary virtue is minimalism. Adding features can be useful for certain niche markets (suspension for downhillers, aero bars for racers) but for the most part a bike is only improved when one can deliver the same (or improved) characteristics of handling, comfort and durability while using less material. Sometimes this is a question of design improvement, but this is rare -- many designs recur over decades (like integrated headset bearings) without ever really becoming essential. More often improvements come from better materials and fabrication techniques.
Take a look at Rohloff hubs.
Take a look at belt drives.
Take a look at disc brakes.
You've already dismissed everything to do with materials, oh well.
Sounds like you just mean: bicycles are two triangles and two hoops... and you would be right.
Strangely that's because the UCI restricted the development of bikes to ensure a level playing field, recumbents were banned in races, as were Moultons with their small wheels and pylon frames, as were the monocoque carbon frames, as were the bikes with farings.
Ultimately, being restricted to two triangles and two hoops means that the manufacturers can only really innovate with everything else.