Why don't I have to season my cast-iron teapot?
You can season the exterior of the kettle to help prevent rust, if you like.  

The interior of a cast iron tea kettle is often rust-proofed through chemicals that accrue during normal use. One of these is lime scale. Repeatedly boiling water, especially hard water, will build a coating of lime scale that will keep rust at bay. 

Another set of chemicals that help reduce the occurrence of rust are tannins. The tannic acid in tea leaves will react with red iron rust on the kettle to produce a more stable, blue-black compound called ferric tannate. To "season" a brand new tea kettle you can save used tea leaves and bags then place several in the pot and adding boiling water. Allow the "tea" to sit for 20 minutes then discard and rinse.

As other answers state, a traditional fat-polymer seasoning of the interior is unnecessary because you do not need to prevent food from sticking to the kettle.