I think a Local WiFi connection without internet for Join will be very practical and useful...
I think there's a heavy use of join to connect devices which are not on us, but still within reach.
Like, mirroring notifications to PC, when my phone is in other room. Or sending file to multiple devices while working on a project. And getting it in few secs or getting notified of incoming calls or SMS.
I think a Local WiFi without internet connection can be perfect for such use. As data won't be send to external servers, So no doubt about the privacy breach. Also it will be faster as you don't have to rely on internet speed.
There is already an app called easyjoin on playstore which works on Local, without internet. Also it allows to control other devices. But it's not stable and is very new.
As we all love and trust Joao, I request if you can add this to our favourite Join :)