The key is that each essay needs to be evaluated and needs to be evaluated using the same scale. If you are trying to measure writing skills then evaluate them based on those criteria. If writing is a very small part of the RA job then this part of the process should be a very small part of the application. Ask yourself what you are really looking for and if it is really a necessary part of the job. If you do not use the essay or you do not evaluate them on a rated scale, you should not use it.
Many selection processes rely on a group process.
Usually the aim of such experiences is to see how students interact within a group. In terms of appropriate assessment this tool is not very reliable or valid. If the goal is to accurately assess a person's performance and role within the context of a group, the best way to measure that would be to ask for feedback from someone who has observed them in such a role. A much better assessment of group skills could be obtained from a coach, a teacher in a class with extensive groups, an advisor or a previous employer. Developing a reference sheet that asks the types of skills you are trying to measure in the group process will give you much better insight into a candidates actual skills in this area.