Out of curiosity, I tried the alternat box-top closing method. While it looks somewhat cool, I'm definitely NOT A FAN.
First, the insertive tab seems to lose its flat integrity when shoved back down into a slot near its crease. Forcing cardboard to curve and buckle back on itself weakens it and then it's just kinda mushy and doesn't hold the opening shut as crisply as it should.
Second, when pouring from a cereal box, I pull the liner up so that it's just past the tabs/flaps, so that when I'm done pouring none of the remainder falls back into the box outside of the liner bag. This becomes awkward with inward folded tabs which snarl and catch at the liner bag if you try to slide it out part way. And if you don't then contents gets trapped behind the tabs anyway and falls back into the box outside the liner bag.
Third, once closed there's an upward facing seam/gap into which things might fall or get trapped. They will fall into the contents of the box when you attempt to open it. (presuming you didn't also take the additional step of rolling closed the liner bag inside, which I never felt the need to do.) While there aren't many bugs in my climate I'd rather not create a situation in which they could easily fall into my food.