Everybody says the dark days started during the N64 era, but I'd actually say it all started during the SNES era. They never really won it by that much, not to mention that they never really started recovering from that time until recently. Worst of all, their profits started eroding at this point. Their install base was decreasing which meant less profits than the NES by far.
As for the N64 cartridges were only a small part of the issue. Saturn had CDs and yet they didn't light the world on fire either. Most PS1 games could not have been that big if for no other reason than the fact it only had 2MB of RAM to load anything on that disc into, all the storage in the world doesn't get around that. Several games if you're just looking at the graphics and basic sounds did not go over 40MB (aside from the awful videos Mega Man X4 could've easily been on N64 storage wise). If storage size was a real issue the DS would be getting raped by the PSP which we know isn't happening. Most DS games are in the range of 8 to 16MB at the most which is the majority of N64 cartridge sizes. It was primarily their royalties and programming difficulties of the consoles in both Sega and Nintendo's case. Everybody wanted to get away from Nintendo mainly due to that as well content control (Duke Nukem 64 had no strip joints, saved women instead of kill them, etc.) which they sure as heck lifted during the GC era. (BMX XXX uncensored on GC, censored on PS2) During the 16 bit era, most developers had originally jumped over to Sega hoping for them to be a salvation until they figured out that Sega as far as royalties were concerned WANTED to be Nintendo. Part of the reason Sony became third party to these companies in the first place during SNES/Genesis was to study the industry at the time. They figured out about the royalties and to an extent corrected them for their Playstation brand. That and Sony literally opened up the floodgates and didn't stop much of anyone from making a game on the system (unless it was 2D...) which lead to one of the biggest libraries in history. Having the system easy to program for didn't hurt either.
As far as bringing back GC games on the Wii, to be honest with you I hope not. The Wii needs NEW, FRESH content, let GC and it's games go for a good while before revisiting them.