From there, Nintendo relied on gimmicks and corporate mascots/IP.
I guess sega was a few years ahead of them on their own timeline.
I’m not sure how successful it was, it was outsold by Xbox and PS2. Although the Xbox was a massive money pit for Microsoft. At least in Europe the Gamecube began to disappear from retail a fair bit before the Wii was out as well. Still, got things like a Wavebird for cheap on clearance though…
Can't play DVDs (PS2, or XBox with the remote accessory,) can't even play audio CDs. Let's remember that this was also an era where half or less of the on campus freshmen had a desktop computer for their dorm, let alone something like a laptop.
That said one could also argue that Nintendo was more focused on mobile at the time, between the GBA and DS, both of which certainly carried them through that era.
I think one could argue that the DS's success alongside the challenges Gamecube had for adoption, led to the philosophy involved in the Wii's design.
I should note the 'other' option that came up back then at college was just tossing a DVD Drive in a computer that they had or had purchased; by that point a majority/plurality of new/recent desktops had enough horsepower to do it, though drives were still fairly expensive...
I think you're underselling the role of their game design expertise. They figured out that there's more to games than high fidelity graphics, a concept which has somehow alluded most AAA game studios.