Why is copper good for tea kettles?  

A better conductor..
As well as easy to work with.
Although it is poisonous.... so should be tinned on the inside, this applies to brass too (which contains copper)

Conduction
Copper is the best conductor of heat and electricity.

Robert, let me get this straight...
Copper is poisonous to humans? What gives then with all the copper plumbing in houses? Is the inside of copper pipe surfaced with something, or are we all just being slowly killed by the water from our copper pipes?

cold water
is unreactive..boiling water less so.

It is not completely true...
that cold water is non-reactive to copper, but yes temperature makes a huge difference.
Although I appreciate the copper bottoms of cooking pots or thicker aluminum with the same result, in the case of e tea kettle I do not see the point of conducting the heat well. Even if a particular spot heats up much warmer than another part of the bottom where the contact with the herat element is not as good, the water will warm up and simply by circulation it will warm up evenly.