As the family members of a recently deceased loved one, you are under no obligation to have a public viewing. Some families will make the decision to keep the casket closed and restrict the grieving process to just a private funeral or interment service.
With that said, there is a reason why public viewings have for so long been part of many cultural, ethnic, and religious traditions. Though they are not always appropriate - especially if the body of the deceased has undergone some form of trauma - a public viewing can be an important way to facilitate the grieving process.
A public viewing is, above all else, profoundly visual. It allows a chance for friends and family members to see with their own eyes a final glimpse of the deceased - something that can provide closure. A public viewing is an important way to help mourners gain acceptance - yes, this beloved friend or family member has passed on, and this passing is final.
A public viewing can have special merit as far as children are concerned. For children who have not experienced loss or attended memorial services before, a public viewing can be a meaningful way for parents or grandparents to explain what has happened and to help them grasp its weightiness and its gravity. Of course, a prerequisite for this is that proper explanation is offered.
Finally, public viewings are significant for loved ones who may not have seen the deceased in some time. If you just saw the deceased yesterday, in full robust health, you may feel more comfortable skipping the viewing, remembering him or her as you saw them in life; not everyone will have that luxury, though, and many friends and family members will covet a chance to say one last goodbye.