QI charging over a large area
Covering the desk in coils will leave dead spots because the current flow in one direction on one coil edge will be opposite to the current flow in an adjacent coil edge. Net ampere-turns is zero = no magnetic field.

It's all down to the value of inductance if you build a large coil. As the coil area gets bigger so does the inductance so this means reducing the number of turns to keep the inductance low. Keeping the inductance low allows you to push significantly more current into the coil for a given drive voltage.

Why do you need more amps for a bigger coil you might ask. Maximum magnetic field density is theoretically closest to the coil - for a big coil and a target device placed centrally in the plane of the coil, the mag field is much weaker hence you need more amps.

However, getting more amps is not that easy - you'll have to probably modify the QI drive circuit to insert a power amp and this might be a bit tricky because the transmit coil is sometimes used as a receiver for signalling from the target device and with a power amp in the way this signalling won't work. So you need to do some research here to see if you can get away without up-link signalling.