Desktops do need better power infrastructure, though something like a NUC could be powered by a small solar panel. A Rpi or ARM-based chromebox is even lighter on the power needs. Haswell (or ARM) based laptops can do 10 hours on a charge and wouldn't even need a consistent power supply.

Not sure what you mean by connectivity -- desktops and mobile devices have the same options: wireless (3/4G, etc), and wired (via wifi for the mobiles). A desktop surely doesn't require buildout of a infrastructure-heavy wired network to have comparable connectivity to a smartphone.