How will it stream from an internet source without internet? Or are you saying you can’t stream from your music library on your local network? 

Via cell phone.

Inet connection goes down and my Sonos hardware can't talk to the mother ship, which btw I find......obtrusive. I can stream , for example, Pandora on my phone but can only BT to a random speaker.

Sonos needs to get out of the middle of hardware I bought and when and how I use it.

Yes , you can stream if you download for example the playlist offline, or you have a offline music library, if that’s the case.

So this means that in the end I cannot stream anything, if I don’t have a internet connection.

(remember wifi is fully working, you just don’t have is the internet provision) 

sound ridiculous it it’s the truth.

Is your router connected to your cell phone’s Internet signal?
 

Your Sonos system is connected to your router, and reaches out through that ‘source’. The controller on your cell phone is merely a ‘remote’, to see what is happening on your system, it doesn’t do anything more than display what is happening on your system. 

Have a read here, make sure your network is setup to work offline, what is key, is your DNS servers on clients (using DHCP) are set to the routers DNS, ie DNS servers are accessible when your internet is down.

Make sure you phone is connected to the local WiFi, not a 4G/5G mobile network as Bruce says above.

Also see the reaction to your post here: 

How would you want this to work? You are using an internet source for your music and the internet connection to your Sonos system is down. While I can see you would be disappointed in your ISP, I cannot see how this reflects badly on Sonos.

The Desktop app works fine when offline (usual limitations regarding music services), but mobile app does not as it needs to get to the Sonos cloud.