Commerce Discount: spend $X, get product free
I don't think avoiding an adjuster or plugin approach here really gains you anything much and it probably creates potential issues - it will likely just make the discount rules confusing as you can't really document the special conditions anywhere on those rules etc (and experience shows over time editors are likely to forget the special conditions and make mistakes with these sorts of hidden logic approaches).

Personally I would approach this by listening to onAddToCart and onRemoveFromCart

https://craftcommerce.com/docs/events-reference#commerce_cart.onaddtocart
https://craftcommerce.com/docs/events-reference#commerce_cart.onremovefromcart

In each of these I would call a function that inspects the order total and either adds the free item (if not already in the cart) if the total is high enough, or removes it if it is present but the order total slips below the desired total.  And you'd want to look at the item total, not the cart total presumably.

To make it editor friendly, I would also add a control panel page that allows the editors to set the cart total threshold and the free product they get if the threshold is exceeded.