It's not that developers didn't wanted an outer join in the physical join, it's just that the physical layer must not think about inner or outer join but just about "how to connect object A with object B" technically.
And you outer joins or inner joins you set them, as you said, in the business model.
But actually your need can be done in the business model. You said your 4 tables act as a single dimension.
So your dimension has a single LTS and you start with your core table. Then inside that same LTS you add your extra tables defining the relationship between them (so outer joins).
You add your 4 tables there and set your joins type and done. The available tables when you click the "+" are based on the relationship you defined in the physical layer, and the type answer you need of left outer join between core and bridge and core and table1 (and maybe bridge and table3, or you keep that one as inner).
Did you already try that option? Isn't it working for you?