I've worked as a product manager (and manager of product managers) for over a decade. I do realize that outsourcing the entire product management role is probably a bad idea, but I do believe that there is still an opportunity for consultants to help companies with specific aspects or projects. I want to start consulting and need clarity on the type of problems companies have that a consultant could help with.
i have seen companies hiring marking research agencies to anticipate consumer / customer reaction to their products, which cost then a fortune... often the loads of data which these agencies deliver in return is also too much to handle, once I saw a consultant recommending a 7 point questionnaire and asking one employee to sit down and call a few hundred customers in a week to get the response. That was much cost effective and pragmatic as well. This might be one thing where consultants can play their part.