How beneficial is attending a funeral in the process of grieving and why? Is there any established literature that indicates that attending a funeral aids in the grieving process? I would like to know if funerals pay a critical role in the grieving process and what makes them important.
So I had a quick look into your question (not my area). It turns out there is long established  journal called "Death Studies" that focuses specifically on "bereavement and loss, grief therapy, death attitudes, suicide, and death education".

From a quick search on Google Scholar for "funerals grieving", I found an article by  Romanoff (1998) that looked like it might provide a starting point. That said, it's not especially empirical (i.e., it is not an RCT evaluating the effectiveness of funeral attendance).

For example, to quote the text:


  Funeral rituals are symbolic enactments that provide meaning- ful and affirming experiences for the bereaved. Funeral rituals mediate the transition of the deceased from life to death, and mediate the transition of the bereaved from one social status to another (Pine, 1989). They provide opportunities for the public display of grief, structures for the delimitation of grief, vehicles for affirming the relationship of the deceased to the community, and
  the continuity of the community in his or her absence (Fulton, 1988) . During this time of transition, members of the social group tend to the bereaved in an outpouring of human support that tran- scends social status ( Turner, 1969) . Postfuneral bereavement rituals, while rare in American culture (McGoldrick et al., 1991), provide structure to the grieving and full incorporation into a new social status ( Goldberg, 1981) .


References

Romanoff, B. D. (1998). Rituals and the grieving process. Death studies, 22(8), 697-711.