I read about the new typescript 2.1 release and figured it should be possible to remove babel from my ReactReduxSpa-derived webpack config, which I tried.
It works, but it broke HMR. This seems to be caused by the aspnet-webpack-react module checking explicitly for babel-loader in HotModuleReplacement:

if (loaderConfig.loader && (loaderConfig.loader.match(/\bbabel-loader\b/))

If I change this line to:

if (loaderConfig.loader && (loaderConfig.loader.match(/\bbabel-loader\b/) || loaderConfig.loader.match(/\bawesome-typescript-loader\b/))) {

HMR starts working again. I added a check for awesome-typescript-loader which I use, the original uses ts-loader. My change might break the original config. Not sure how to do this correctly.