He’s bedded the mix on slate most likely. Granted it does not look great , but i disagree with it cracking , he may have added latex or crushed stone to the mix effectively making it concrete. It could last a hundred years.
Agreed , there should be an overhang as the water now will just soak in to the brickwork .
Why didn't they suggest to take the stack down to below roof level and close the roof???
If the chimney is not used, what's the point of it?
Agree with others, without any overhangs and dripping channel, that repointing will be short lived.