As long as you don’t use it on a gas stove, you should be fine.

Not any more, their quality has increased recently. Not that I care, wife and I did without them during our engagement.

Part of the argument is that better heat conduction means that you can run the nozzle cooler resulting in less heat conduction to the cold side (above where you want the filament to melt) so I guess its "cooling" in a sense too.

From what I understand their idea seems to be that since most heating occurs at channels they act like hotspots and therefore it would be much better to drain away heat from them directly.

This is different from creating transistors on a diamond substrate.

No idea if it actually matters. Is this a single digit percentage increase in thermal conductivity by messing with a finicky, temperamental process? I don't know. What the paper writers are proposing is under the limit of when transistor structures break down, but not by much.