Chromecast only works from iOS for apps that have integrated with the Chromecast SDK. Like Netflix and Youtube.
Maybe the EU can ask Google to open Chromecast up so Apple can integrate it into iOS. Then you can use it from any app without needing special integrations.
Apple has all the information they need, available publicly, to implement an OS-wide Chromecast client. They haven't done so because they don't want to.
