It is normal to feel stuck when dealing with a Human Resources program that is stuck somewhere in the Industrial Revolution. Although job descriptions still play a role, the whole notion of a job is undergoing many changes in today's workplace.
Growing numbers of companies are focusing less on structured jobs and more on the best way to organize in order to complete the work that has to be done. Rather than designing highly detailed job descriptions, there is more emphasis placed upon the individual employee's knowledge, skills, and abilities, and the best way to match them with the work to be done.
Many studies are finding that this trend originated less from the leadership of an organization, and more from large numbers of employees who seek more flexibility, variety, and challenge in their work, and it sounds like you are part of this group. This means that you should meet again with management, but instead of expressing dissatisfaction about current job descriptions, your "job" is to try to let them see the widespread advantages of flexibility and increased focus on work rather than on jobs.
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