Just make a small change - 1/8" left of centershot, then 1/8" right of centershot, then back... That should do it. For the record, I'm not ruling out that you can find a scenario where your method works, I've just never seen it and too many people nowadays are saying the same thing.
Also - just so we're on the same page, I am viewing all adjustments from behind the bow. For a right handed archer - moving the rest right is in towards the riser...
If your way does work - I've been wondering if there's a possible combination of horizontal nock travel and the string power stroke combined with how long the rest stays up, drops away immediately, or if it's a fully supported rest like a biscuit or a blade that could cause different reactions.
Actually - not entirely correct, at least in my view. The BH tipped arrow will stabilize in a straight line and eventually fly true exactly the same as the FP tipped arrow except in extreme cases where the vanes can't overcome the broadhead drag. What happens though is that the BH tipped arrow stabilizes on a different line / vector from the bow so it still hits off course.