Well, it's a long story.
From what we in the community know, Superbot (the developer) was given a shoestring budget and very little help from Sony in securing licenses for third party characters. As a result, they were largely at the complete mercy of rights holders. This is horribly evident in Raiden and DmC Dante, who were pretty much demanded.
Heihachi, Big Daddy, and Isaac Clarke were the only third parties who worked with Superbot to make their characters feel great. Namco wrote all of Heihachi's dialogue, 2K lent them Ken Lavine for story and direction, and EA sent over tons of material to make Isaac as accurate as possible while letting them use pretty much whatever they wanted from it.
Konami wanted Raiden because maketing, and he wasn't allowed to use any of his weapons because spoilers. Same for Dante. We have confirmation that Lara Croft was pitched but SE wanted TR to come out before Lara was playable in anything else. Abe from Oddworld was DLC, paired with Dart, but after Isaac and Zeus (from God of War... yes...) didn't sell, plans were cancelled. We only know this from concept art and Oddworld developers accidentally letting it slip in a tweet.
We know there was a Final Fantasy item in the game that got removed thanks to leaked pre-release screenshots of the debug menu item list.
Now this next part is all potentially my memory going fuzzy, but I'll throw it out just in case. IIRC, a leaker showed up and bought some credibility by showing some concept art that was later released. They ranted about how licensing was an utter mess and they legitimately tried to make everyone happy but the money and the support wasn't there. Activision didn't want Spyro to seem "better" on any one platform because Skylanders and had no plans for Crash so they weren't able to secure them. (This is somewhat supported by an unverified Activision intern who did an interview, but they claimed it was more about money.) FF13 was "big" at the time so SE basically told them Lightning or STFU. Ryu Hayabusa was supposed to be her rival. Those two would have added development time, and they tried to push them back as DLC. Tecmo didn't want Ryu to be DLC, so thanks to the Rival system, they were both cut. We don't know the veracity of this because there hasn't been much pre-release info datamined save some screenshots, one video, and concept art. Many others were difficult to obtain because nobody "wanted their characters to be shot in the face with real guns and stabbed by serial killers." They also said that basically the only time Sony stepped in was to tell them they couldn't do something. They also said that Vita crossplay hobbled the entire game. Imagine the 3DS development drain, but now they had to be 100% cross-compatible.
These next rumors are unsourced but I've seen them passed around and they're sad enough to be believable.
They also claimed they tried to reach real hard for just about anything, IIRC Krome (of Ty the Tasmanian Tiger) were really excited about the project. Croc was also supposedly sought. Both fell through, allegedly because Sony stepped in to say "No." These are probably hearsay but I'd buy it.
Really, the entire game was a perfect storm of poor timing, no support, and awful logistical choices. I fully believe if the Vita was buried, Crash and Spyro remasters were coming, FF13 was forgotten, and Lara's game was out, we'd have had a very very different roster.