Because Sony tried this twice in the 90s/early 2000s with Sony v Bleem and Sony v Connectix and lost both times
You may as well ask why Microsoft doesn't go after Xbox emulation: its the same reason. Nintendo are outliers in terms of being aggressively litigous, and so far Nintendo hasn't actually brought emulators to court; all of the emulation devs have settled because lol who has money for legal fees. Sony COULD decide to harass the shadps4 people on it, but if the shadps4 people decide to actually go to court, Sony would lose.