Why do so many wheel bolt patterns / pitch circle diameters exist?

The number of bolts is determined by how much torque will be applied to the hubs, which is a function of power, weight, traction, gearing, and lateral forces, with a safety margin built in. Small economy cars (low power, skinny tires, light weight) usually have 4 bolt wheels. Light trucks usually have 6 bolt wheels. Heavier trucks have 8 bolt wheels. Everything else will have 5 bolt wheels. Sometimes an economy car with a high performance variant will have 5 bolt wheels for the sake of standardization. 

The French (Renault and Citroen) used 3 bolt wheels on a lot of their cars long after everyone else abandoned them. Saved weight, and cost, but not a very safe approach.

As for why manufacturers use different bolt spacing, they just do :) American manufacturers went to 5 bolt wheels for full size cars about 90 years ago, and for the most part still use the same bolt spacing they chose back then. Companies usually standardize internally based on the class of car, but as you've noticed they don't always. If the car is based on a new platform they will probably have to make new hubs anyway, so there's no cost savings for using the same bolt pattern.

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