1. They wanted (and needed) to hit handheld pricing
2. They wanted a relatively expensive 3D display technology (so less budget for other hardware components)
3. They wanted to make a profit on the hardware itself (so lower overall budget per console, to maintain profit margin)
4. For the scope and type of game they were envisioning the 3DS to run the hardware is sufficient.
5. Gamecube emulation is not easy. The 3DS can run native games similar in complexity to the GC, which is a more reasonable expectation.
5.1: Look at other mobile hardware from 2011, like mobile phones, they are much more powerful than the 3DS yes, (also noteably more expensive, without 3D screen, controller, DS hardware for backward compatibility etc.) and they can't emulate GameCube either. Ie. mobile tech in general was not at that point yet.
6. Gamecube was released 2001, 3DS released 2011, it's a 10 year gap not 15.
7. Battery life, "legacy" hardware can be used not just to save cost, but also for some efficiency gains -> longer battery life.
I could go on. But honestly a bit of research/understanding how consoles/computers work and how they evolve over time would've told you that the question is sort of weird. Not why the 3DS is weak, even for the time it was by no means cutting edge, but the speciifc comparisions you choose to make make no sense to demonstrate this "weakness".