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I don't think this reluctance comes from critical psychiatry as such. It has always emphasised the integration of mind and brain. It's a mistake to think that mental symptoms are not based on a neural substrate. Critical psychiatrists can understand the wish, as much as anyone else, that neuroscience could solve the theoretical and therapeutic problems of psychiatry.
The problem is that fulfilling that wish is "intellectually bold" in Bullmore et al's own words. They are fearful that psychiatry will be cast "adrift from the core principles of medicine". They can't understand why anyone would want to prescribe psychotropic medication without thinking that symptoms were "somehow related to abnormal synaptic signalling between nerve cells".
Correspondence in reply (eg. by Andrew Blewett) sees through this argument. Neurohawkishness seems to be on the defensive.