The forces on a bridge are a combination of shear and torsion. In this situation and according to Fine Woodworking report where the test method was a shear action, PVA is the best best. It is more forgiving than hide glue which requires an 'absolute' fit. When replacing components, unless you are some sort of genius, a perfect mating surface is often unachieveable; there will be a few low spots etc caused by the cleanup...
PVA has convenience above everything else. It is an industry standard and as RonS says, does not creep and unlike hide glue is not brittle.
I admire people like Dave Means who uses hide glue. If I could see any benefit over PVA to doing so myself I would also use it. However, a University degree in craft based woodwork and metalwork with modules in timber technology, the history of the classical guitar, materials science etc leads me to conclude it's not worth the effort FOR ME. I salute you all and especially Frank Ford who writes so eloquently about this old technology.