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I don't see any advantage vs the shutter button unless your wearing gloves or something.
There are huge advantages. It means you can lock focus and shift the camera slightly off a focus point. One such technique is called focus-and-recompose, but it has limits.
It means that you can deliberately set one focus in a field of changing objects (people milling around a central figure for example) and not have to focus for every shot.
It means you can focus stack.
It means you can focus and meter in any order. You can also compose before during or after those (within limits).
It means you don't have fiddle switch autofocus on and off at the lens.
I set it as soon as I discovered it available and never looked back.
You can always reset focus simultaneously with the shutter button by coordinating your thumb and shutter finger. It's extremely easy and natural, once you get used to it.
Don't leave yourself at the mercy of the shutter button.
Backbutton focus is very creative and returns control to the photographer (assisted by tools at their discretion), which is where it ultimately belongs.