Nintendo tried this somewhat with the Gamecube as well, had a system more capable than PS2, developer friendly now opting to use CDs instead of cartridges, and did try to get more 3rd party mature support with exclusives from Capcom like RE4 and others.

Well, the GameCube launched 18 months later in Japan than the PS2, 13 month later in America and 18 months later in Europe. Until then, the PS2 had a big advantage both in hardware base as in the library of games.

The propriatary mini-DVD format also wasn't that developer friendly with only 1/3 capacity of a single-layered DVD or 1/6 capacity of a dual-layered DVD.

If a developer really wanted to make a game for the Gamecube, they would've found a way to do it regardless of the mini DVDs. The PS2 was also difficult to develop for but developers put up with it cause the PS brand was too strong to ignore. The Switch is getting ports that have zero business to run on that hardware. I'm sure if PS had mini DVDs it still would've got a ton of 3rd party support just cause of the brand PS being too strong and Sony being so pro-3rd party and help accomodate them unlike Nintendo. The mini-DVD problem was overexaggerated too, many games didn't need more than 1.5GB, and if they did they could simply make a 2nd disc, which wasn't that much more expensive to implement unlike cartridges.