From my memory, the laptop looks like a bulky 2000s model. It doesn't seem to be used for anything else than the occasional movie by the point in time the series is set. It is shown in a scene where Elliot and Darlene torrent and watch an in-universe slasher flick that explains where Fsociety got their characteristic mask design from.

Considering that Elliot doesn't need to bring a computer around for his work and don't do any hacking-related activites in public for obvious reasons, then I guess the desktop just makes more sense to use at home as it is more powerful, more easily upgradable, fixable and the hard drive can be removed quickly. And also, big screen.