I wonder if you've ever used a Chromecast based on this criticism.
For a standard Chromecast, you open the app on your phone, then press the cast button, then the device you want to cast to, and the the device begins to stream the media independently of your device. You can shut off the device you used to start casting and it doesn't matter because Chromecast is pulling the data on its own.
On some websites such as YouTube on PC, you also have a cast button and you can press it, select the device and it'll start playing. you can get this button to work on all kinds of sites, and a lot of open source software supports it to a degree such as VLC, Peertube (through a plugin), and Jellyfin.
Using google chrome you can cast your current webpage or your desktop, but that's not the standard use of Chromecast.
It takes some finagling, but you can cast from Jellyfin to a standard Chromecast right from your phone.
The latest version out is Chromecast with Android TV, which is really nice (for now). It's running a version of android and has the play store, so you can set up the Jellyfin android TV app, and stream from your home server without requiring a domain name or https like you do to stream properly on straight Chromecast.
The big issue with Chromecast in my view is that it's a Google product which means 3 things:
it's proprietary, which has many risks coming from that nature and a crappy largely hidden API
it can be shut down any moment if they desire (see google graveyard), and being an always-on device it's possible they just brick it on the way out
it will suck up as much data as they can from you to try to sell you more crap