Because they suck at it. Their MP-centric output during PS3 was mediocre at best. And now it's gonna be infested with mtx-galore. No thanks. Stick to your strengths and what you do best.
That’s not true.
They made Warhawk, which is the best online game ever made.
Problem with their PS3 era was they shotgunned so many shooters it spread the online base thin. MS just focused on Halo and Gears, Activision was COD, EA was BF. The drips and drabs were cut off fast like MoH, Crysis and any other MP games they made.
If Sony was going to go MP, they should had focused a lot more effort into maybe 1-2 franchises and stick with it. PS3 era they had Resistance, KZ, MAG, SOCOM, Warhawk, Haze exclusivity from UBI. Then they tried to latch PS3 onto those big battle games like Planetside and Dust 514. By the looks of it they tried more shooter franchises than all the other key companies combined.
It scared off Sony so much all they did for PS4 is KZ Shadowfall at launch. They they ditched MP shooter franchises since then (a decade).
They are trying the same thing again with all their GAAS games coming out. Not all are shooters. They still got GT and baseball. But GAAS games usually revolve around sports or shooters. Since Sony doesn't makes other sports games aside from baseball, it'll likely trend to shooters again unless they try something different like deck building games, mobile, gem matching games, Diablo kind of game etc....