How much shorter?
If only a tiny bit, no they're not trash.
The trim length is, in most cases, really an arbitrary figure.
As long as your cases aren't too short, and are all the same length (to promote consistent crimping), they should be good for a long, long time.
"The gift which I am sending you is called a dog, and is in fact the most precious and valuable possession of mankind" -Theodorus Gaza
Baby Jesus cries when the fat redneck doesn't have military-grade firepower.