why am I confident they would? because NES and SNES which were powerful, followed norms for the time, worked. Nintendo only started failing when they went 'off road' and used cart in a time when everyone was using CD. Nintendo's biggest failure is because they don't keep up to date with tech
You seem adamant that the N64 being a cart-based system was "nintendo's downfall", but the N64 wasn't a failure and devs
could and did fit games on the carts, or there wouldn't be any. It was a good system with a lot of power (the most powerful of the 5th gens, in fact) and the reason for 3rd parties being wary is because carts aren't novel, the architecture was a bit difficult, and nintendo just historically has had issues courting 3rd parties due to region locking and the 'difficulty' involved with granting development licenses.
As I said, when the N64 came out, CD-based systems might have reasonably been seen as a gimmick themselves—consider all the ones that
utterly failed, like the 3DO, the CD-i, the Mega CD, the FM Towns Marty, the PCE-CD, and the Neo Geo home console. Some combination of expense and poor software, coupled with the speed of the drives, made for a very hard sell. Sony's name and Sega's name were almost enough to carry them, but the Saturn and PS had their problems. Sony was doing their best to court 3rd parties, so games flooded to the system and its familiar, easy-to-use architecture and gave consumers more of a reason to buy it.
The Nintendo 64 wasn't a failure (though it was a mere lukewarm success at best), the cart-based idea made sense at the time it came out (1996), and the raw technical power of the system was enhanced by the speed that you can access data in ROM carts. The gamecube was a decently powerful system too, but it just had too much working against it (and eventually Sony and Nintendo switched places on the Proprietary First-Party Bullshyt Scale).
Many of these developers and publishers begrudgingly put up with Nintendo when they had to. When Sony gave them an out they ran away as fast as they could and a lot of them aren't really interested in returning in the first place.
If tomorrow Nintendo put out an sequel console to the competition companies like EA would still be bullish on them until it's proven that Nintendo's customer base could power the sorts of games they sell.
This is a very good point here, and illustrates how there wasn't really any one decision that wrecked the GCN or dampened what could have been a knockout blow with the N64. Technical power and ease of development mean very little in the face of a giant third-party revolt.