try creating a variable, but don't put anything into the variable.
Then in the Set Field Value or Update Item action, insert your empty variable into the value section.
I just tried it on a test list and it worked without a problem. I also set the field to "Required", still worked. Enabled content type, set the field to "Hidden", still worked...
Does it work if you "overwrite" with something else than empty?
I created a new list, added a field called Country (Single line of text). I then create an item and set the value for that field to USA.
Next, I created a workflow and all it has is a Set Field Value action with the Country field selected and the value left blank.
When I ran this workflow, it cleared it out.
Can you try a new workflow on that list with just the Set Field Value action and see if that works?
If it does, this suggests that maybe in your other workflow, it's not getting to this action.
I see that your and my definition of a "simple text field" are completely different...
However, I just tested it with a form library and clearing a promoted field really doesn't work (I also tried "Update List Item" with the same result).
It does work if you use the "Update XML" action: In Infopath click the arrow on the right of your field name and select "Copy Xpath" in the context menu.
Use this xpath in the "Update XML" action and select "Replace Node contents".
I also noticed that clearing the field in Sharepoint manually does not work either: You have to open the Infopath form, clear the field and save the form, then it works. So probably this is "on purpose".