Why doesn't indexing syntax broadcast?

Why don’t these do the same thing?

julia> getindex.([[1,2], [3,4]], 1)
2-element Array{Int64,1}:
 1
 3

julia> [[1,2], [3,4]].[1]
ERROR: syntax: invalid syntax "[[1, 2], [3, 4]].[1]"

This syntax doesn’t exist and there are issues around implementation, see the discussion here: https://github.com/JuliaLang/julia/issues/19169

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