Jon, for me the difficulty would be if I really felt like crying and wanted to, but felt unable to. If I didn't feel like crying, then not crying wouldn't be a problem. For me, crying has been an integral part of grieving.

Crying does make me feel better, because walking around wanting to cry and forcing myself not to is a strain. So there is some relief when I do it. Also, there are stress hormones and proteins found in tears, so crying may be our body's way to eliminate some of these stressful compounds.

Article on health benefits of crying: Gender differences and the health benefits of crying