In your daily life, what things do you do, that you could do with the aid of a so called "modern PC", that you do with something else?
A legacy system, NG system, your cell phone etc.
I think right now, people who only consume content (i.e. play games, watch video, listen to music, talk/converse with others) can totally fulfill their needs with an iPad, smart phone, gaming sytem or other non-desktop PC device.
For those who need to create content (i.e. do video editing, programming, electronics interfacing, AUTOCAD design, multitrack music, 3d rendering, graphics work) the desktop PC is still very relevant. This is because the desktop PC still offers the most CPU power for the buck and also is highly configurable (i.e. with a musician you might need to have several pro-level sound cards installed for multiple-ins and outs plus a MIDI interface).
This will probably change as things like iPads become closer and closer to being just as powerful to desktop computers.