that's much more complicated. Plus you only have to hold the af on button down if you want to track focus with servo, if you are on one shot then you press it just once. Having af on be the only way to focus means only ever pressing one button, the method you described involves 2 button presses.
Theres many scenario's where I use back button focus -
My daughter is on a swing and I am at the side of her, she's swinging back and forth constantly. I want to frame her on the moment where she is on the fulcrum of that swing - I could follow her swing but i'm moving as well as her and it means keeping my focus point on her face as she swings back and forth - might not be the right composition.
So I frame it then I wait for her to reach the right spot and then focus using the back button. Then I just wait, each time she swings into shot i press the shutter - i now never have to refocus, and I don't have to recompose - if you did your focus with the shutter it would refocus each time she swung in and you could focus on the wrong thing. Here's an example shot:
Other examples would be that she stays in the same place but is pulling different expressions, maybe moving her head from side to side. by focussing with a back button you can focus just once and then snap, snap whenever you like - never refocussing always keeping the same exposure and composition