What policies are those?

There's no evidence that gamers would have jumped ship without the games to incentivize them to do so (games and price are the two biggest factors by far in determining a system's success), and there's no evidence that the big third parties would have jumped ship anyway regardless of format. We have interviews with Square staff where they routinely single out the N64's cartridge format as a reason for switching to the PS1, so we do know that format was the reason why arguably the most important PS1 game came to the PS1 in the first place. Enix almost certainly switched over for the same reason. CDs offered over ten times the capacity of an N64 cartridge at one-tenth the cost, which made them extremely attractive to many established publishers who wanted to make grand adventures (the N64 was not known for its strong selection of JRPGs). Capcom and Konami released games for the Saturn as well as the PS1 before the former tanked in Japan and the latter hit the big time, which is in keeping with their prior behavior of supporting two systems, but their support for the N64 was minimal, again almost certainly due to the expensive, low-capacity cartridge format (both of them released far more games for the GC than they ever did for the N64, even if they weren't putting their biggest and best games on it).

Every bit of evidence accumulated over the past 23 years points to Nintendo's decisions when it comes to hardware design being the reason why they've struggled with third-party support on their home consoles after the 16-bit era.

"Let's us all remember GameCube was disc based and suffered an even worse defeat against PS2, and we can't put the "brand" as a big advantage for PS there since Nintendo had a longer image on the market and much more fans."

The PS2 was riding the momentum of the PS1, while the GameCube was also having to split the remainder of the U.S. market share with Xbox. Oh, and the GC's discs were mini-DVDs with a capacity of only 1.5MB, only a bit over double that of a CD, a third the capacity of a single-layer DVD, and less than 18% the capacity of a double-layer DVD. Many PS2 & Xbox games would not have fit on a single GC disc (even some PS1 games wouldn't have). Few developers were in the habit of splitting games across multiple discs, and nearly all of the relatively small number of multi-disc releases after Gen 5 weren't actually multi-disc games, with the second disc usually being a bonus disc with extra features (though a tiny handful of post-Gen 5 games did have the multiplayer on Disc 2, and FFXIII was a 2-disc release on the 360). Also, a developer that worked on Max Payne cited the GameCube’s lower main RAM (24MB, vs 32MB for the PS2 and 64MB for the Xbox) as a reason for why they didn’t port their game to the system despite releasing it for the PS2 and Xbox, though as far as I'm aware of they were the only ones citing RAM as a concern.

In any case, many of the most popular third-party games in Gen 6 were either PS2 exclusive, or were released on the PS2 & Xbox but not the GameCube. The GC missed out on huge titles like Final Fantasy, Metal Gear, Grand Theft Auto, Kingdom Hearts, and Star Wars: Battlefront. While it wasn't the only factor, the GameCube's format was almost certainly what kept many big-name games off of the system. As a result, while the GameCube did have arguably better third-party support than the N64, it was still inferior to that enjoyed by the Xbox and especially the PS2.

Nintendo was interested in the disc route, but they weren't happy with how much control Sony would have had over licensing, and subsequently revenue, on the SNES CD. Apparently the terms of the deal would have given Sony a great deal of control over both. So Sony wasn't an entirely innocent party in that debacle like everybody thinks. Nintendo dumped them for Philips. Then they decided to go with cartridges. When they went to optical media for the Gamecube they partnered with Panasonic.

Nintendo accepted the deal, and then single side decided to terminate the contract. So they were fully at fault.

I'm pretty sure you know about the policies from Nintendo on NES and SNES but a quicklink for you https://books.google.com/books?id=XiM0ntMybNwC&pg=PA110&lpg=PA110&dq=the+draconian+policies+of+nintendo&source=bl&ots=1YvtCgsvLl&sig=ACfU3U1N4c0c-tOfQR9wqrK2-4L66X1m9g&hl=en&sa=X&ved=2ahUKEwi4vv3H7oLkAhUoo1kKHdjPAjUQ6AEwBXoECAcQAQ#v=onepage&q=the%20draconian%20policies%20of%20nintendo&f=false

https://nerdtrek.com/nintendos-restrictive-licensing-history/

A lot of these policies were products of the NES era, were strictly for the US market, were implemented as a backlash against the market conditions that destroyed the American video game market in 1983, and most of them were rolled back by the time the SNES hit the market, such as the five game limit. More policies still were rolled back or ended as the 16-bit generation went on. Konami disbanded Ultra Games in 1991 because they no longer needed to go through a shell corporation to release more than 5 games a year. And within a few years, publishers and developers were complaining about Sony's licensing restrictions.

So several of those devs were ready to jump ship. CD-ROM is a reason for it? Sure, but Sega CD had a CD, Saturn had a CD and that didn't made Nintendo lose. It was an effect of Sony involvement.

Sega also had multiple failed consoles. Sega NEVER had a successful console in Japan. The Mega Drive came in third to the Super Famicom and PC Engine in the 16-bit era in Japan. The Saturn ran neck-and-neck with the N64. The Master System didn't even really register in Japan. And console add-ons have likewise never successful save for cheap ones like the Super Game Boy. The Saturn was an underpowered train wreck of a console that was technically incapable of 3-D, developers had to manipulate sprites to create 3-D on it. There's an interview with the producers of Panzer Dragoon Saga that explains all that.

Ease of development is a huge thing. Game developers would rather spend time and money fleshing out a game rather than fighting with a console's architecture just to make it do what you want. 

Why would developers jump ship from Nintendo to a company that had a long track record of failure? Sony offered them the space they wanted without Sega's baggage or the Saturn's bizarre architecture.  

You underestimate just how huge of a value proposition CD-ROMs were. They offered 80 times the storage of a cartridge at pennies on the dollar. Furthermore, you could use as many discs as you needed for a single game with minimal increase in manufacturing costs. I guarantee you that far outweighs any hurt fee-fees over Nintendo's policies. Had Nintendo had CD-ROMs, their track record of dominance in video games would have made them the clear first choice, especially with the loyal backing of Square and Enix.

Square did everything they could to stay with N64 and only left when it became clear that the N64 didn't have what they wanted for FFVII, namely the storage necessary to contain a huge game and the cinematic FMV scenes. FMV is extremely space-intensive. They specifically cited storage space as the issue. They weren't "under the lash" at all. Nintendo actually treated them very well given their role in the success of the Super Famicom. 

We always go the way of all the success of Sony is the result of competitors doing bad, no merits to Sony.

Xbox had better HW and DVD and didn't get many of the games PS2 received.

Xbox was an American console. Japan is notoriously nationalistic when it comes to cars and electronics, save for outliers like the iPhone. Japanese developers knew this and didn't waste their money on developing for it. The Gamecube did far better than the Xbox in Japan and got far more Japanese games. 

Momentum per Momentum, NES came from SNES and sold much lower than the other due to Genesis (and it wasn't due to CD as well), N64 came from SNES. So the least momentum piece would be PS1 and it still won.

NES had no effective competitors in the market. SNES had two major competitors and still smoked both of them. Plus they had the Game Boy, which crushed every competitor it ever had. 

Depending on the incentive games will release on platform with limitations, RE4 released on PS2 even though promissed not to because of the limitations as an example, and the Switch ports are another.

Incentives only go so far. Microsoft moneyhatted quite a few Japanese games early in the 360's life to try and boost the system in Japan. After a few games actually turned into financial failures despite Microsoft's money, the developers in question moved them to Wii or PS3, which were more popular, in order to salvage the situation. We almost lost the Tales series for good because of Microsoft moneyhatting Vesperia on 360. 

The Switch's RAM profile is based on what Capcom asked for.