Trouble with DIMENSION_PROPERTIES - ssas

Question

I'm doing some exploratory work with tiny test dimensions and cubes. I'm hoping to finally fully understand SSAS's concept of a "dimension attribute", which I find pretty incomprehensible, though I've used SSAS for years without really getting to the bottom of it.
But that's too broad a question. My problem now is this:
I've created an Employee dimension. Key column is EID (int), Name column is Name (varchar). OK, my naming conventions aren't brilliant (but good naming conventions seem to be very difficult in SSAS dimension design, given the fact that all object names are exposed to users).
There is also an attribute called Salary.
What I'm trying to do here is explore the possibility of a "dimension leaf-level property". Not really "dimension attributes" in the sense SSAS uses them, though the only way to implement them is as dimension attributes. What I mean by a "leaf-level property" is a non-aggregatable "attribute", with the same cardinality as the leaf level (or, in any case, to be treated as having the same cardinality). I don't want to aggregate by Salary, for the purposes of this exercise: I just want Salary to be available as a property of each leaf-level member of the dimension. A bit like an extension of the Key Column and Name Column properties.
I'm familiar with this common way of showing member properties:
WITH MEMBER Measures.ESal AS Employee.EID.CurrentMember.Properties("Salary")
SELECT
Measures.ESal ON 0,
Employee.EID.EID.Members
ON 1
FROM $Employee
This works. To prove that I'm only returning members from the leaf level, here's the result set:
(It makes sense that a member property for a non-leaf level might not have a value - and I've read that in this case, MDX simply throw an error rather than showing values for the leaf-level members and nothing for non-leaf).
But trying to use DIMENSION PROPERTIES causes an error:
SELECT
{} ON 0,
Employee.EID.EID.Members
DIMENSION PROPERTIES Employee.Salary
ON 1
FROM $Employee
Result: Query (4, 22) The [Employee].[Salary] dimension attribute was not found.
If I put the hierarchy and level in, though, it works (though SSMS doesn't actually show anything specified in DIMENSION PROPERTIES; as I'd heard already):
SELECT
{} ON 0,
Employee.EID.EID.Members
DIMENSION PROPERTIES Employee.EID.EID.Salary
ON 1
FROM $Employee
Result: just like before, but with no ESal column (obviously).
Two questions:
Why does the Salary attribute have to be addressed as an attribute
of dimension/hierarchy/level Employee.EID.EID? Surely it's an
attribute in the dimension? (I find the way SSAS/SSDT implements
multiple hierarchies deeply confused and confusing)
What is the point of DIMENSION PROPERTIES? Do other clients
actually show what it returns? If so, isn't it then a nightmare to
test this code?