Sony threw down the gauntlet against 2D games early on in the life of their first PlayStation console. Very few 2D games were released in North America (while Japan got many more early on). I can think of only a handful of 2D titles to see release on the PSOne in the first year or two.

Rayman, Street Fighter The Movie, and Raiden Project were all 2D and released early in the life of the original PlayStation, if not a launch title themselves (depending on where you lived your launch titles may have varied).

Rayman, I think that was allowed through because Ubi Soft held so much publishing power (even more now). I don't think Sony wanted to risk making them mad and them going Sega Saturn or N64 exclusively. While we an look back now and think that is a silly concern, back then, Sony had every reason to believe either console maker to be a major threat to the success of the PlayStation.

Next was Street Fighter The Movie. I think this was allowed through, again, due to the publisher. Sony was not stupid, Street Fighter was a massively popular franchise and Capcom had many others to follow. PlayStation being the only 32-Bit console without a Street Fighter port was probably not even on the potential list for approving 2D games.

Next we had Raiden Project. This one was probably allowed through early on as a benchmark offering. Showing the PlayStation could do 2D and do it well, even better than many arcade games. Sure, the two titles on offer were not exactly all that taxing but the franchise was gaining in popularity - plus this was the only home port of Raiden II we would see.

NBA Jam Tournament Edition is another early one to see release. Just sheer popularity of this franchise guaranteed it got approved, regardless of its 2D styling.

Rayman is the only early original 2D game to see release on the PlayStation though. Had it not been for Ubi Soft publishing it, I think it would have been denied just on the basis of being 2D.

Sony's focus on 3D is what forced Sega's hand with the Saturn, and their adding custom chipsets upon custom chipsets to the hardware. This complicated programming for the console and caused a lot of developers to abandon the hardware early, or not even attempting anything on it.

I can only imagine had Sega foregone adding those chips to the hardware and focused on the Saturn being a 2D powerhouse. They had the cartridge slot which would have easily allowed adding custom chips that way - though probably not fast enough of a transfer speed to make it "manageable".

Arcades were dying when the Saturn came out, and were all but dead before the Dreamcast came out. That makes me think they may have been able to eek out a much better position in gaming had they focused on 2D with the Saturn before going hardcore with 3D on the Dreamcast.

Sega's biggest problem though, was their stringent behavior of being greedy with their home ports of their arcade games. Namco ate Sega's lunch in this regard. When you bought Virtua Fighter 1 or 2 on Sega Saturn you got as close to the arcade game as possible in the home at the time.

When you bought a Namco arcade game port you got not only the arcade game as close as possible but much more. Maybe more characters, texture mapped graphics, new modes, updates to the basic game, etc.

Had Sony not had such a tight grip on what they would allow on their console as far as 3D or 2D, I think 2D would have faired much better in the 32-Bit era. Sony certainly changed the direction of gaming with this tactic. Whether they meant to or not.