the only thing that happens when you use a wider strip - you can end up with different sized blocks depending on how many cuts you make. Not a big deal if you trim in between.
When you use 1", it exactly replaces what goes into the seam allowance. So if you start out with a 9" piece, no matter how you cut it and resew, it will still be 9". If you use wider, and make 2 cross cuts and 1 top to bottom cut, you'll end up with 10" x 9.5" block, because each cut will add .5" to that dimension. Again - not a problem if you trim.