First: The presentation of data and framework and the changing of one's options are two different events that are not causally linked.

Now to rebut:

I do not pretend to defend all union action. I only protect them insofar as that union action redistributes money, a relative resource.

You have not shown unions improve the economy by lowering interest or inflation.

Only BoC can change interest rates, and corporation changes the price of goods. So by your own definition, if improving the economy can only improved by lowering interest rates or inflation, unions cannot do it.

However, increased labour costs can be eating by corporations profit margin (if available) instead of passed to the consumer.

Unions increase affordability, a word you have not stated once in your reply. Unions increase labour costs, but they increase purchasing power faster than increasing costs, as such affordability (relative resource) increases.

You have not shown inequality is the cause of low wages.

It is by definition. Inequality is the distribution of income between owners and workers. When a sale occurs, part of the value goes to owners, part to labour; the larger the owner’s share, the lower the relative wage. Money being a relative resource, high inequality and low wages are simply two sides of the same coin.