Hi,
ok, this says it all:
"So one storage type will have products for only one customer."
Coming back to your original question "why customer is not considered as a criterion for putaway and pickup?" - "But as work process, the warehouse is divided in to storage types based on customer."
This is not what we assume what a storage type defines. One storage type for one customer? That's why standard structures don't support your requirement.
Brgds
Juergen