I only cut remaining 'scraps' from finished projects into 2 1/2" strips, if the pieces aren't big enough to be a fat quarter. My fabric cabinet has;
a shelf for flannel and pre-cut 8" batting squares that will one day be in a rag quilt,
a shelf for larger cuts (think 4 yds or more)
a shelf for smaller cuts that stand on edge like books (1/2 yd to 4 yd)
and the top shelf is 2 1/2" strips and fat quarter size cuts
If it's smaller than 2 1/2" I get rid of it. I tried saving smaller pieces, but never used them. You'd be surprised how many patterns can use 2 1/2" strips!