The double squares is a fun design, but I can also see the downside of it. Those little "flaps" would be oh-so-tempting to use as "pulls" to pull the quilt up onto oneself. All that extra pulling & tugging in one condensed area would make those triangle pieces more prone to snapped stitches, pulled threads, worn out fabric & batting migration.
If you are planning on a different design (am I the only one who thinks it looks like a flowery swastika???) but still like the 2 squares, I'm wondering if perhaps you could add 4 reinforced sharks teeth to the binding (the corners of the square would then be the same color as the binding) by cutting it extra wide in those parts so that you don't have to worry about batting migration, the fabric would be double thickness & you would only have those small bits sticking out so they wouldn't be as tempting to tug on.