It's not.
The available choices were Intel, AMD, Nvidia, or going ARM.
Intel is not a valid choice, their iGPUs do not supply enough graphical power. They would have needed to combine Intel CPU + Nvidia or AMD GPU.
Nvidia is not a valid choice, unless they were going ARM because Nvidia does not have a license for x86 architecture. Nintendo made the choice to go ARM, hence Nvidia Tegra in the Switch.
AMD, by process of elimination, was the only valid choice (unless they were going ARM). Unfortunately AMD CPU performance is abysmal when considering perf/watt or hell just straight up perf. So Sony/MS made the best of it, the CPU was going to be shit but at least they could get 8 cores of shit and let the devs figure out how multithreaded game code works. At least they could also get a decent performing GPU and AMD was willing to give the whole thing to them for a song which let them hit their launch price targets, unlike Intel/Nvidia who would charge out the ass.
So yeah, Jaguar is a piece of shit, but it's there for many good reasons. $399 launch price of PS4 is one, low power usage allowing for much less cooling required and smaller console form factor is another. The biggest reason though is that they could get a pretty decent AMD GPU without paying Nvidia ungodly sums of money.