Why is that Flutter does not have a web target? Everything is nice and fast about it, it's a shame that after building a cross mobile apps, you'll app to start the web app from scratch using another platform.

React Native doesn't either. Only via the third-party React Native Web project[1]. Which I'm sure something similar for Flutter can also be achieved if desired.

[1] - https://github.com/necolas/react-native-web