Why does milk and white chocolate have different tempering temperatures?

When it comes to thermodynamics, you always have to consider the whole mixture, not its components separately.

This is true of everything, not just chocolate. Mixtures behave in their own way - not entirely independent of their components, but the interactions within them are complex enough that you need some serious chemistry to start predicting melting or boiling points of simple mixtures (e.g. the boiling point of a mixture of known proportions of two liquids, as long as they behave close enough to an ideal liquid). For something as complex as chocolate? Forget it. Just go in and make empirical measurements.

And why does nature behave so? Imagine the solid chocolate as a quilt. All the components have to fit exactly together to make the pattern. But there is no quilter to assemble the pieces; they float around, bump into each other and, if the conditions are right, the bumped sides stick together. Then other pieces start fitting into the already-combined mini-lumps, and they have to be the right pieces too - in a quilt, you cannot fit a hexagonal element into a space with 90° angles. This is why chocolate tempering is easier when "seeded" with tempered chocolate - you already have the first crystals onto which the new molecules have to latch in the right pattern, while without seeding, you have to rely on providing the conditions under which the spontaneously formed initial crystals are mostly of the form you want.

In this model, milk chocolate and white chocolate will have different "quilt patterns", so they will need different conditions for the sticking-together (crystal growth) to happen. And temperature is one of the most important conditions in melting/solidifying, so it is no wonder that you need a different temperature for the two.

Tempering chocolate, like many physical and chemical processes, is less about making one result possible and others impossible, and more about making certain results more likely than others in such a way that, over the enormous number of particles involved, the desired outcome dominates. You never get 100% formation of type V crystals, you just get enough that the type V crystals become the majority of the 'seed' crystals that then provide scaffolding for more type V crystals to grow on themselves as the chocolate cools further.

I don't know specifically how the absence of cocoa solids affects cocoa butter crystal formation in white chocolate, but chemically speaking, it's not unusual for a different environment to result in favourable conditions for different kinds of crystals, or for those favourable conditions to change differently with temperature relative to the original environment. Perhaps the carbohydrates that make up a large portion of the cocoa solids provide their own nucleation sites, or they inhibit the formation of certain types of crystals by getting in the way physically.

It's because white "chocolate" is not actually chocolate and does not contain any cocoa solids. It's not simply a different ratio of ingredients like milk and dark chocolate are.