I have use 2" strips for French binding, and then I hand sew the invisible ladder stitch on the back. Works fine.

I always use 2" for my binding. I fold and iron in half. Then machine sew to front, turn to back and hand stitch. Works good.

I use to use 2 1/2" but am now using 2".

Two Inch Binding
 

I usually use 2" binding and it works fine. I even stuff it sometimes t make it firmer. No need to make scant quarter inch seam, just make the stitches smaller to be sure it is secure. Press on .