This behavior for the 'Department' attribute is persistent for all NPIOS except the Project object.
It affects Ideas, Applications, Assets, Other Work, Product, Services.
You do not really need to set the default on the "Department" attribute.
The 'Department OBS' attribute should be the attribute that you are using on the General Properties page of the investment.
When you associate for example the Idea Object to the Department OBS (the menu option Administration - Organization and Access - OBS), you get a new attribute in the object that is a special attribute and that is also linked to the investment financial properties page.
When the new attribute is created it will have the the name of 'Department OBS' and a description of 'Attribute created due to Department OBS Association'.
You can set the default value on this field if desired.
Then when you create a new instance, on the create page, if the attribute is there, it will show the default value.