How to dynamically change columns in a Matrix or Chart

Actually there is a way to accomplish this without the new fields parameter option. Bascially you need to build a table to use as the slicer listing the values of all the columns you need in a single column. Take this data as an example:

To be able to filter the item, colour and type columns, we need to create a table to use as a slicer listing all the values & the column name (& and order column for sorting purposes.

To create the new table, you can append the columns in Power Query or use the following DAX:

Select Column Table =
VAR _item =
    SELECTCOLUMNS (
        FactTable,
        "SelColumn", FactTable[Item],
        "ColumnName", "Item",
        "Order", 1
    )
VAR _colour =
    SELECTCOLUMNS (
        FactTable,
        "SelColumn", FactTable[Colour],
        "ColumnName", "Colour",
        "Order", 2
    )
VAR _type =
    SELECTCOLUMNS (
        FactTable,
        "SelColumn", FactTable[Type],
        "ColumnName", "Type",
        "Order", 3
    )
RETURN
    DISTINCT ( UNION ( _item, _colour, _type ) )

to get..

Next create relationships between the SelColumn field in this new table and each of the columns in the fact table:

Then a simple SUM measure and the following measure to use in the matrix:

Select Column Measure =
SWITCH (
    SELECTEDVALUE ( 'Select Column Table'[ColumnName] ),
    "Item", [Sum Value],
    "Colour",
        CALCULATE (
            [Sum Value],
            USERELATIONSHIP ( 'Select Column Table'[SelColumn], FactTable[Colour] )
        ),
    "Type",
        CALCULATE (
            [Sum Value],
            USERELATIONSHIP ( 'Select Column Table'[SelColumn], FactTable[Type] )
        )
)

or if you also need the grand total (which I don´t think makes much sense since the result is multiplied by the number of columns selected):

With totals =
SUMX (
    'Select Column Table',
    CALCULATE (
        SWITCH (
            SELECTEDVALUE ( 'Select Column Table'[ColumnName] ),
            "Item", [Sum Value],
            "Colour",
                CALCULATE (
                    [Sum Value],
                    USERELATIONSHIP ( 'Select Column Table'[SelColumn], FactTable[Colour] )
                ),
            "Type",
                CALCULATE (
                    [Sum Value],
                    USERELATIONSHIP ( 'Select Column Table'[SelColumn], FactTable[Type] )
                )
        )
    )
)

To get:

 I've attached the sample PBIX file