You’re missing the whole story here. Was the Game Boy well designed? It was a smash hit upon release, but everybody immediately complained about the screen quality. The thing sold and sold and sold because it was inexpensive and just plain fun, bad screen notwithstanding. By 1996 however, it was woefully old, and the Game Boy Pocket sales were soft when it came out. Pokémon saved Nintendo’s bacon and gave them leeway to develop the Game Boy Color, which was also old and criticized upon release, but it again had Pokémon.
It’s more complicated than a simple good or bad checkmark whether a thing is popular or not.
I would call the original Game Boy well-designed but put the GBC in the same "Underpowered, but a surprise smash hit capturing that era’s sensibilities" category as the Wii.
With the tech at the time, the Game Boy wasn't going to have a better screen without seriously compromising battery life. Case in point, the Sega Game Gear which was graphically way better than the Game Boy but died fast if you took it off the wall plug.
The GBC didn't have the same excuse; it was so many years newer, and it offered very little over the Game Boy other than a color screen. And its color screen still looked like a joke next to a Game Gear. Given how much newer the GBC was than the GG, I doubt Nintendo couldn't have made a handheld with Game Gear-quality graphics but without the awful battery life.
But it doesn't matter, because the GBC had an awesome games library and people loved it.
It was the pragmatic choice at the time: the screen was reflective and featured four colors (really, shades of grey), but that was enough to allow the system to run for several hours on four AA batteries. It's closest competition, the Game Gear, featured a backlit color LCD, but it ran through its six AA batteries in an hour or two at most. There were other also-ran handhelds in that era (Wonderswan, Neo Geo Pocket), but the Game Boy was by far the most dominant system of that era. Nintendo didn't face any substantial competition until 2004/2005 with the PlayStation Portable, and even Sony didn't do all that well with its two portable units (the PSP sold okay but game sales dropped off once the system was hacked, the Vita was a dismal failure in both hardware and game sales).
The Atari Lynx was the other one that came to mind. I agree with you, the original Gameboy was well-designed. I had one of course being over 40. It was the Nokia brick phone of handhelds. Yes, I was envious of the Game Gear, but most of the attention was on the Gameboy anyway so you could safely ignore its existence at the time. Portable anything back then was still quite the novelty. And the games on the Gameboy were fun. Tough to beat a game of Super Mario Land or Tetris.
It’s more complicated than a simple good or bad checkmark whether a thing is popular or not.