(I have a friend who used to have a job drawing cut plans for diamond wafers at Kyocera Unimerco.)
My first thought is that the high conductivity doesn't necessarily mean it won't, being loose and hand-wavey with terminology because I don't know it, fracture with thermal shock, like non-borosilicate glassware (don't change the temp. too quickly) say, or ceramics (don't introduce too much of a temp. delta across the item, e.g. heating on a hob)?
Second thought is 'is it too much better than copper', in the sense that is the conductivity no longer the limiting factor? Copper is prized (and actually bloody hard to get these days - afaict everything on Amazon is copper-coloured or at best clad aluminium) because of fast 'response time' to change in heat, as you adjust the burner or pull it off the heat altogether. Conductivity also helps with even heating of course, but it doesn't help it cool particularly, which is limited by the rate of loss due to convection through air (and what's being cooked, which is what we want to limit if we're hoping for it to cool) and radiation?