The opportunity here is not just convergence but multi modal. We have bits and pieces in the current world but frankly it's a big stinky mess that is poorly integrated. Most of this stuff is just horribly limited and single vendor walled gardens.
A good positive example or how things should work is spotify. I regularly switch between my desktop, laptop and phone and the spotify instances seem to be aware of each other. I accidentally started playing music at home while at work today because my laptop spotify was still targeting my home desktop. Just works.
What matters here is that spotify is available on multiple platforms; it moves files around for you as you need them. All you do is sign in and it will serve you your music, playlists, etc. In the same way I can continue reading a e-book on my phone that I was reading earlier on my Kindle. Browser state is replicating across platforms as well.
The logical next steps would be devices where after authentication, your apps and data are just available and adapt to the device in a way that makes sense. Right now setting up a new laptop is a chore. You have to worry about installing stuff, configuring stuff. signing into stuff, backing up stuff, etc. Ideally all that goes away and you basically just pick up a device and start using it with zero effort. Or better even, the devices are integrated into the environment and simply adapt to you being there. Some apps won't make sense in all form-factors but many do.
Ever walked into a hotel room and after briefly fiddling with some alien hotel entertainment system simply watched netflix on your laptop? I watched netflix on a recent transatlantic flight and ignored the entertainment system 20 centimeters from my nose it's just better and I charged it using usb-c from my laptop. So, I walked out of the plane with a fully charged phone. What if those devices in hotels, planes, etc. would basically provide you all your stuff after a simple signin? Walk into a hotel and all your digital stuff is already there by the time you walk into the room?
And yes there are all sorts of concerns with privacy, security, etc. All solvable problems.
For device manufacturers this would liberate them from selling only one or a handful of devices per person. You could turn phones into fashion accessories. They pretty much are already but why just have one phone when you could have one to match each pair of shoes? Why fiddle with your phone when you step in your car that these days might have a huge touch screen and plenty of computing power. Convergence is much broader than just your phone + laptop.