Yes, Zigbee is the way to go. But the point is there shouldn't be any internet involved. Using the internet protocol on wifi is the stupidest way to do this kind of stuff and leads to dumb crap like your washing machine phoning home.
I mean, it's obviously a pretty good product in terms of effortlessly providing networking to a device in a way that an average home user can manage. Everyone has wifi.
That being said, a better architected device would probably just use Bluetooth and your smartphone as a controller. I don't think many average home users could tell the difference.
I have a label printer that works like that and I hate it.
I'm not sure what the better answer is now that I am trying to think of one. Maybe all I really hate is how shitty and lack of control the app is. It requires me to turn on location, and does who the f knows what on the network between the app and brother. I do not want to have to turn on location to use a label printer. No matter the tech excuse about detecting proximity, something has simply gone off the rails at that point.
But using Bluetooth as a local connection, I guess that's OK if the protocol were just open and I could choose the app to use with it.
Devices with web servers have that one big plus, which is that you use your browser, not someone else's browser.
Make the same sort of genericization on bluetooth and that would probably satisfy a good number of use cases.