I've been thinking about this for some time; what could have been done to make the GameCube a better console? In Nintendo's interest to create a console designated purely for gaming, they succeeded, but in doing so they drove away a lot of casual gamers. The main problems I can see are:
1. The console was not backwards-compatible. This is something that really irritates me about every nintendo home console- the fact it can only play games of its generation. I heard the 64 was supposed to play SNES games and I was quite cut when i found out otherwise... That was definitely a good point of the PS2, that you could play all your old fav PS1 games on it, and the Xbox360: all the Xbox games still work on it.
2. A Lack of built-in networking hardware. Although not a major design flaw as some other aspects were, it still made some kinds of gaming awkward. For instance, the only way you could play a multi-console game would be to go out and buy a modem (and for me the only option is to order a modem from Nintendo Australia, and anyone I want to play with has to do the same- too much hassle). I don't know about other people but doesn't split-screen gaming just get plain irritating after a while, especially with 4 players? Additionally games with higher levels of detail had to use lower-resolution textures in these modes and even had to drop some things completely from some games in multiplayer mode. For instance, a multiplayer Resident Evil 4 would be impossible on one console- generating that level of detail for 2 screens would cause some serious drops in framerate for the console. Besides, how satisfying would it be hunting down Garradors, Novistadoors and plain ol' Ganados with a teammate?
3. Absence of a DVD player. Its probably been covered before, but by not including a DVD player, Nintendo had effectively aleinated anyone considering buying the console as a cheaper solution to wanting a DVD player (lets not forget back in 2001/2002 DVD players weren't cheap). I am aware that including a DVD player would deviate from the idea of the console being "purely for gaming" but I dont believe it was a very intelligent move. Unlike Sony and Microsoft, without having a DVD player meant less justification for buying a console.
4. Specially designed optical media. The DVD MiniDisc idea seemed cool at first, but I really don't see what they accomplished by choosing this format as a medium. I think I read somewhere that it was supposed to be a format very hard to duplicate as opposed to the PS2/Xbox standard DVD discs, which is sensible because that way the manufacturers won't be short changed by cheapskates. However, let's not forget that these discs would require specially made machinery to create them in the first place: they would then work out to be more expensive than normal DVDs since they cannot be mass produced with the rest of the DVD optical media.
Getting back to the cheapskate point; some people probably found that an appealing aspect of the PS2/Xbox - the fact you dont really need to buy any games at all- just copy them, which may have made the console look more attractive since all they had to do is get it then copy off friends/video shops. Naturally not everybody did this, since it also required a MOD chip, and I know lots of people who still prefer to buy their games rather than copy them, still it would look nice to have that option open from a consumer perspective.
Lastly, although the DVD MiniDiscs hold 1.5 Gigabytes it sadly just doesnt seem to be enough. The Xbox/PS2 discs could hold a grand total of 4.7 (single layer) or 8.9 (double-layer) Gigabytes. This would have pleased the developers of the time, since they could throw all the levels, pre-rendered movies and music on, not to mention those delicious little extras like "behind the scenes" or "making of" or "interview with the developers" videos without having to worry about storage restrictions. One upside of the GameCubes discs though is the very fast loading times. I have not seen a PS2 or Xbox game load nearly as quickly as a GameCube game.
*phew* thats a load off my mind... I might have missed a couple of points and I'll update if I come to realise that. In the meantime feel free to disagree with anything I posted. I tried to keep it as objective as possible