They went into the 7th gen like they went into the 6th gen - with an absurdly difficult console to develop for and no real help for the developers to capitalize on it. This had been a problem for the PS2 but the PS2 was also cheap, widely adopted, and the games were standard-def so the dev costs were manageable.
The PS3 was the opposite of all that so when the plopped this monstrosity onto the market, not only did no one buy one, but studios looked at the difficulty and cost of developing for it and noped out. AFAIK it was the SCEA and SCEE (American and European) studios that wrote a ton of the middleware that eventually made it into dev kits which then salvaged the PS3 as a feasible development target for Japanese studios. Westoids are what made the PS3 and, as a result, they got put in control of the brand once the PS3 made a comeback (Xbox shitting the bed with kinect also helped). There's a reason why Mark Cerny gets to talk about the Playstation technical specs while Ken Kutaragi lives in the cuckshed.