Point is, 5 influence is worth nothing in the game. It won't give you any benefits, and it will not be enough to help you cross the boundary to Friendly in any significant way. If Consulates is +20 and Papal Primacy is +15, this will bring you across the boundary even without the Pledge to Protect. As such, pledging has become meaningless.
It would have made more sense if Consulates was +15, Pledge +10 and Papal Primacy another +10 and then some other effect to PP to make it more useful, like easier religion spread to city states. This way, only with the combined effect of all three would you have permanent friendship with a city state, making them all relevant if this is a strategy you aim for.