I am glad you are open to constructive feedback.
In my opinion, these high level process maps are utterly useless. They don't add any value whatsoever because they are overly simplistic, don't really recognize all the interfaces between processes and are easily glossed over. They seem to exist solely to appease misguided external auditors who "like" to see something like this to tick a mental box they have.
I agree with you 1000% on this.
If you want to do something that really adds value, forget creating a process map such as this. Try to describe in TEXTUAL form the processes and their interfaces in the system. Obviously, you can not put all the details there, but the primary and secondary interfaces. For example one thing that your process map does not contemplate. Customer wants to URGENTLY change the delivery method and address for an order. Your process does not have a DIRECT interface between order management and shipping. Guess what? In an URGENT change order scenario, that interface needs to exist, at the risk of creating customer dissatisfaction. A description of such processes interfaces would help educating the workforce about the quality system of the organization.
Good luck.
It's funny you mention this. Our sister company basically does what you're saying graphically. They have a cross function flow chart for each process showing the inputs and outputs for that process. By looking at the inputs and outputs, you can see the interactions of that process with the other processes. It shows more interaction than the simple diagram that I showed. I've contemplated going that direction, but you've convinced me that it's the way to go.
Thanks a lot Sid