This:
babel ./src/MyTypescript.ts --out-dir ./wwwroot/js/
doesn't work (no error, just '0 compiled').
.babelrc
contains everything that Babel 7 need to compile typescript with webpack babel loader: preset "@babel/typescript" and plugin "babel-plugin-transform-class-properties" (pair which works for me with current babel 7 rc01).
Here is an answer:
babel ./src/MyTypescript.ts --out-dir ./wwwroot/js/ --extensions '.ts,.js'