It would be good if the Eufy Security App (iOS version) has an option to cast the live streaming (and recorded videos from Events) to Google Chromecast. 
Eufy Security App - Eufy Video Doorbell - Live Streaming to Google Chromecast
It would make more sense if it live streams to Google Smart Display or Echo Show than Chromecast, since Chromecast is a dumb device and needs a smartphone / desktop to “cast” to it.
Exactly. The suggestion here is simply to use the Eufy Security (iOS) app to have an option to cast the live streaming to Google Chromecast.
Shouldn’t be too difficult. I’ve implemented Google Chromecast casting capabilities in my apps. 
Your idea for Google Smart Display can be another option that they add. But I’m more interested in seeing Eufy Security (iOS) app with an option to cast the live streaming to Google Chromecast.