I thought Check 21 (enacted back in 2003) was supposed to eliminate that, allowing digital check images to substitute for physical copies during the clearing process. My understanding was banks (or even sometimes merchants) just scan in the paper checks on receipt these days and process everything electronically.
That could very well be... I remember many a late night run to the airport to help resolve some crisis back in the 80s/90s, to keep them canceled checks flying.
https://en.wikipedia.org/wiki/Check_21_Act