Another example: I make a selection of a round object, I notice the tool is still on "add to selection" after painstakingly tracing around a pattern I wished to cut from the middle of the round selection... I can't simply complete the selection to change it to subtract because the pattern is inside of the already selected area...
YES you can!
The Polygonal Lasso Tool does not care about about what you have "painstakingly" tried to select to remove form an image...............it only makes a selection no matter what the selection option is set to! The selection options only affect the active selection.
Lets say I'm about to make a selection with the Polygonal Lasso Tool. I have the selection option set to "subtract from selection". Before you start or while your in the process of making a selection, take a look at your cursor........please note that there is no minus sign on your cursor..............until you complete the selection..............then the minus sign will appear on the cursor. The selection options are only for and will only affect a completed active selection. No matter what the selection option is set to, it will not affect what you have "painstakingly" selected from an image or what you plan to do with the selection.
So here I have made a selection with the tools selection option set to "subtract from selection"

I have made an ACTIVE selection around a round object.
The selection option has made NO difference on the selection and what I can do with it.
But lets say I want to ADD to or SUBTRACT from my active selection.
Since I already have the selection option set to "subtract from selection"...........lets make a rectangular selection at the bottom......
Look...it subtracted from the center area of my active selection.
Now lets try adding to the active selection.
I set my selection option to "add to selection", lets make another rectangular selection ant the bottom.
Look.........it added to the outside of my existing active selection.
No matter what you have the selection option set to when you start making a selection or what you plan to do with the selection..........it doesn't matter unless your planning on altering the active selection.