I think you answered your own question with your point about Neville unless I am not understanding well. Being able to identify an issue and point to a failing requires a different skill set and qualification than applying said knowledge to oneself. Neville's inability to coach as in transfer his message across, create the right environment, man management, be tactically inventive, etc ... has nothing to do with whether or not, he can actually identify those problems and see them in action. The latter is what he needs to be a pundit and his managerial career does nothing to suggest he lacks in those areas.
When it comes to Carragher, being unable to control yourself and having a tendency to lose your temper says nothing about his ability to see those issues and diagnose them. For one to assume so, we have to believe that humans are perfectly logical creatures with no separation whatsoever between what they think is right and what they do in any given circumstances.