ThinCap,
I feel your pain. This has been a common problem in my organization as well. But that does not mean that it is normal nor should it be.
I am (supposed to be) responsible for managing the workflow and backlog for the piping and drafting teams in my organization. I have been fighting an uphill battle ever since being asked to take over the role, as most of the managers above me still find it easier to bring any and all work directly to whoever is available to do it. The reason being time and an inability to adapt. They believe that it is just quicker to bring it to whoever is available to work on it rather than letting me allocate the work to the proper individual. The problem with this though, is that it leads to poor quality work, excessive rework, inconsistency, and errors. Some situations I have faced are:
1) P&IDs given to civil drafters (with no knowledge or training on P&IDs)
2) Electrical one-line diagrams given to structural drafters (with no knowledge/training in anything electrical)
3) Pipers given civil drawings (no knowledge or training)
4) Employees completely unfamiliar with the project being given someone else's work to finish (no clue why certain things were done the way they were)
5) etc.
And while I'm all for cross-training employees to give more flexibility, this isn't what is happening. The managers "need the drawings quick" so they bring it to whoever is available, which I think is more poor planning on their part than anything. It also violates a principle of management known as the unity of command. Employees should only have to report directly to one supervisor. Otherwise, you end up with a completely inefficient organization because the subordinates have no clue who to report to, there becomes overlap among instructions and communication suffers greatly, and a conflict arises between managers.
I would continue to emphasize how important it is to maintain that unity of command principle, and ensure that the right people are given the work so as to not increase your risk of errors and rework. Because it will end up costing a lot more money to the company in the long run if those things happen consistently, rather than taking a little bit more time and doing it right the first time.
"The only limits in life are those which we impose upon ourselves."