The key is in the name, Physically Based. The whole idea behind PBR is to base material inputs on real world and observable values. This makes it easier for artists to create materials that resemble the real world as they can just look up values, for example most metallic objects have 1 metallic (because there metal) and 1 smoothness (because the microsurface is smooth) and then you just input the RGB and your away, you can then add increased detail to the material through changes in the roughness and metallic maps to simulate paint and scratches. The overall advantage, in that case it is easier to be more accurate and more detailed in materials.
One of the best benefits to PBR is it allowed for metallic objects that look metallic. In reallity metallic objects tends to have really dark diffuses with a lot of that color going into the specular (hence a the specular is tinted). They also reflect most of the incoming light. In traditional renderers the closest they would get was a tinted specular and a high specularity.
Compare the metal of the skyhook in Bioshock infinite to an stylised PBR object that uses metal:
Another benefit of PBR is that due to it relying on environmental lighting from reflection techniques such as cubemaps it allows materials to render in many diffrent lighting environments with no changes to the textures. In traditional materials it was common to change the diffuse color based on the environment you placed the object, but in PBR the shader handles all that for you .
Overall it just allowed more control over materials allowing developers to hit higher quality with less effort and allows engines to render a wider range of materials with no changes across a wider range of environments in addition to very little performance overhead compared to traditional rendering. There is likely many other benefits i have not mentioned. But the short of it is once PBR is implemented there is not really a need to use traditional rendering as PBR can do all that and do more whilst giving a quality boost in the process, hence why larger engines completely replaced there material pipeline with PBR,