Most of those studios simply underperformed and were not financially sound for Sony to maintain. If your games aren't going to sell well they should at least receive high praise and generate conversation about your platform. Most of those studios failed to do any of that.
Cambridge should have been shut down long before it was. That was always a mediocre studio at best. Killzone: Mercenary and RIGS were the last gasps of a studio that was probably already on its way out. After all the subpar games they released those last two games needed to be phenomenal and they were not even close.
Liverpool was simply not making money. I know a lot of people point to their legacy but much of that legacy was thanks to the games they helped publish. Similar to Japan Studio. As time went on Liverpool became just another racing studio for Sony. Making the Formula 1 and Wipeout games. The former never did well and very much overlapped with Gran Turismo. The latter was a great franchise but it just started failing to grab much attention compared to its earlier years.
Zipper was a really good studio prior to acquisition. After they were acquired they went downhill for some reason. Their games over the next 6 years did not do well at all and the critical reception to them was far lower than what they did when they were independent.
BigBig was a sister studio to Evolution. It was founded by the same guys who made the latter. When Sony bought Evolution, BigBig came as a packaged deal. I doubt Sony was ever that interested in them in the first place. They never did anything really noteworthy.
Incognito was a very different case. Sony didn't want to shut them down. That was a situation where the studio just experienced not one mass exodus of staff, but two. Back to back. The first group formed Eat Sleep Play and the second formed Lightbox. Interestingly enough, Sony partnered with both independent studios upon their founding. There were so few staff left at Incognito that Sony was faced with a choice. Close the studio down and cut their losses or try to hire so many staff to work at a studio in Utah that you're basically starting from scratch and building a whole new team. Either way, what Incognito had been was gone. The talent and culture evaporated pretty much overnight.
Evolution was in a similar boat to most of the other studios. It had just been failing to produce. The MotorStorm franchise started off as a hit but over the course of several games the critical and commercial reception declined. Then they did Driveclub, which had so many issues prior to release that they had to delay the game a whole year. Even then, it released with a lot of issues. It went on to sell 2 million copies but the damage was done. The critical reception of the game was much lower than anticipated even after a 1-year delay and that delay would undoubtedly end up costing Sony more money than they felt would have been worth it. It didn't help that Evolution, like Liverpool before it, was another racing studio. Racing games have been in decline and just don't have nearly the kind of pull they use to.
It's also worth pointing out that many of the staff who were laid off from Evolution went to work for Codemasters. They were given their own project within the studio called Onrush. A game that did so poorly that most of the former Evolution staff were let go from Codemasters too, including the former director of Driveclub who also directed Onrush. The remaining staff were settled into support roles at the company. Some feel this result vindicates Sony's decision to close Evolution.
Another important thing to remember is that most of these studio closures happened during Kaz Hirai's run as head of the company. The PS3 era saw Sony in a very poor financial situation. Not just PlayStation but the entire company. Hirai employed a lot of Western business practices to get the company back on track. This included trimming a lot of fat. An example being Sony Online Entertainment, which had been bleeding tons of money. I don't remember the exact amount but it was startling how much of Sony's money was being eaten by one group within Sony's entertainment divisions.
One thing that Sony has made clear over the last decade now is that if they're putting a lot of money into you, then you need to produce. Either your games sell a ton of copies or get high critical reception or you do something that no one else in the company does. They'll give you chances but not nearly like they used to. Sony wants the PlayStation name to be associated with quality across the board.
As far as why Sony bought Housemarque, it's because they see current talent and more potential in the studio. Their last five games have a combined Metacritic average of 82 with three of them scoring in the mid to high 80's. Their most recent release was an 86. They also do the kind of games no one else in Sony's stable does. For a studio that has only ever done lower budget arcade-like shooters, Returnal was impressive for their first go at a bigger budget title. A lot of that game was outside their comfort zone.
