does not have the position for that "direct report" you requested, because the management believes that it is your task and one headcount is adequate, therefore, no other resources were planned for it either, eg. computer, salary, benefit......
You need to find out why you 聽信慫恿, if "A" suggested something not in alignment with your mindset, would you still follow her suggestion? Your mindset is to have a direct report under you so that you do not personally work on the task assigned to by others who are "at the same level as you" (include A), you can push the work to the "direct report", right? but you find out that even you get the the direct report, you still need to do work for A, for people at the same level as you - this is the source of your disappointment.