I'm with the folks who say it's largely about the games themselves. Lots of good stuff for the DS, and I'll be getting a 3DS soon so I can get the new Rune Factory and Harvest Moon games when they come out.
Could the design be better? Maybe. But I've played with the DS a lot and have never thought, "Gee, I wish this was a different shape." And I never balked on buying it because of what it looked like. It fits in the hand well, and I like that it closes up because I feel like the controls are protected when I'm carrying it around (plus the suspend on close function).
There are specific games that are not designed well for the controls--I can't remember the name of the game, but I remember one game where I was sort of struggling to press buttons and use the stylus at the same time -- but that's more about bad design than bad controls. Most games use the controls well, and the ones that use the touch screen well do it to great effect (physics games where you draw in the various apparatus you want to make things work properly come to mind). I especially like the games that play with ALL the features, like the microphone and such (read the article on this site called "Rub, Wiggle, and Blow" IIRC for more on innovations used in DS gameplay).
I guess they could come up theoretically with a better design but on the other hand, I've never felt awkward using it or ever felt like it was a bad thing to play on, so why fix what isn't broken?
And I definitely wouldn't want it to look like the picture of the Gameboy in the OP. That looks less portable because you can't close it and it doesn't fit into a pocket or pouch as easily as the nice smooth rectangle the DS is, and I'd miss having 2 screens.