I don't know if desktops have a future, or if even local computing has one. Maybe a portion of "personal computing" ends up only done on mobile devices, and some of the rest of it moves to public clouds.

There might not be a business case for companies to produce chips & other hardware for desktops. So, lets equate buying desktops to buying low-end servers for all practical purposes. As computing gets cloud-ier, is there a business case for low-end servers either, when a high-end server can be virtualized to get the same result?

If we are stuck with power-sensitive mobile devices & virtualized cloud instances on high-end servers as the only businesses that sustain, FPGA's only play is on the servers. You'd expect lots of heterogenity in the workloads there, more than on desktops. Reconfiguring many FPGA's very frequently? Not sure it would fly, even with a small selection of applications vetted to not be damaging to the FPGA.

You can do personal computing with FPGA's with Adapteva boards. How safely can you reconfigure its FPGA, after you have managed to code for it?