Summarize table with dynamic filtering

OK. We can certainly compute distances without needing an extra calculated table in the model. For example,

Closest Profile =
VAR E1 = AVERAGE ( Survey[Element1] )
VAR E2 = AVERAGE ( Survey[Element2] )
VAR E3 = AVERAGE ( Survey[Element3] )
RETURN
    MINX (
        TOPN (
            1,
            Profile,
            ( E1 - Profile[_Element1] ) ^ 2 +
			( E1 - Profile[_Element1] ) ^ 2 +
			( E1 - Profile[_Element1] ) ^ 2,
			ASC
        ),
        Profile[Profile]
    )

You can make all this dynamic without a calculated table:

See attached.

Kudos to AlexisOlson for asking the right question to move this forward!

Rather than TopN do what you want:

Avg Distance Rank = 
    RANKX(
        ALLSELECTED(Profile[Profile]),
        [Avg Distance],
        ,
        ASC,
        Dense
    )

and use it in the visual filter?