Originally, all consoles saved game progress to cartridges: NES, Sega Master System, Game Boy, Game Gear, SNES. When PlayStation came out, Sony had to come up with a new saving solution since CD-ROMs were read-only. That solution was an external memory card, which was also used by Dreamcast, PS2, and GameCube. People weren't happy about having to buy another expensive accessory on top of the system price, but there was no way around that.
Microsoft changed the game completely by including a hard drive in the Xbox, which was ground-breaking and an awesome solution. Saving your game to the hard drive was hassle-free and saved people a lot of money in the long run.
As for flash memory (which is what Wii uses), it was still new technology at the time and very expensive. People were just starting to use USB thumb drives back then, and no one could even conceive putting flash inside a console in 2001.