Ah, so is the question 'are all inserts made from carbide', or 'are all carbide tools based on inserts'? The answer in both cases is 'no'.
Most inserts are made from carbide, or mixes thereof, but there are other types. Two that spring to mind are:
PCD – polycrystalline diamond for high speed machining of non-ferrous materials – up to 3000m/min; that's about 112mph
– I've never used them as my lathe doesn't run that fast
CBN – cubic boron nitride used for machining hardened steel – I have used these to turn fully hardened silver steel, about 64Rc
In both cases the inserts are eye-wateringly expensive, £25 to £50.
Regards,
Andrew