I have had every type of computing device, including pre-smart phone PDA's, and ultimately when I need to do something that isn't mediated by an "app", I will always gravitate towards doing it on an actual computer.
Now - while I do prefer a laptop as my primary machine - it is essentially a desktop, as I typically use it 90% of the time attached to either a dock at home or the office, with external screens, keyboard and mouse.
(Heck - my latest machine only gets about 75m of battery life... it is more a luggable than a "work-at-the-beach" kind of machine (i9, lots of ram, etc.) - and I am perfectly happy with that arrangement)
Most people really do not need the dedicated device, whether it's a laptop or desktop, to use the Internet they way they want to.
Any limitations on smartphones are either ergonomic or entirely artificial.
Assigning tasks to devices can be done due to the capabilities of each device but also due to other factors, like what behaviour you want to influence. For example, if you want to spend less time doom-scrolling/on social media/whatever, moving these tasks outside of the computer you have in your pocket and into the computer you need to sit in front of helps.
In fact, it kind of runs the other way: even my "portable" "real" computer is terrible as, say, a camera, or level. It's a bad GPS navigation device, both due to the form factor and it's entirely lacking the hardware for it (technically they can have this, but very few do).
There are lots of things my phone can do that even my laptop, let alone my desktop, practically can't.