Spotify Connect lets any spotify client act as a remote, and lets you hand-off from one sink to another.
The primary benefit for me is that a Connect client is actually connecting to spotify itself - it's less output sink and more headless client. So if I start spotify playing, and then close my laptop, it can sleep properly without interrupting my Connect device.
I don't want to use a custom firmware image. I like the firmware provided by Google, and the monthly security updates. If I were to switch to a custom build of AOSP, I'd need to sideload Google Play Services (by downloading it from a source I trust less than I trust Google) and would also no longer get security updates.
This way you can send any audio from laptop/phone to the stereo over lan.
Not sure why you would want to limit yourself to the service of a single provider. (What value does Spotify Connect add, if any?)