Chromecast works because your phone/table/pc sends it a link which it then loads. Great for stuff you can get to via a link. Sadly not everything can be accessed like that and, as you say, it's not always convenient to control it.
Roku boxes are much, much better IMO. You can get all your streaming services, eg Amazon Prime, Disney+ along with Iplayer or youtube or loads of other free services. If you have a Plex install you can access content from that too. Controlled via a remote control (included) your phone, via an app, or any 3rd party controller that can talk to the api (eg Home Assistant) - You can also cast to a Roku if you want
Google home is the Google equivalent of Amazon Alexa - you are right, different thing.
405 line? Couldn't you cook your dinner with it whist watching it? or would it cook you?