How Does Statement of Purpose Play a Role in Graduate Admission?
I doubt that "competitiveness of research area" is much of a factor, even for doctoral admission. They are looking for candidates who have an appropriate background (mostly from the CV) and a good probability of success in the program (mostly from LoR). The first bullet in your list is always the critical part. But the second point should simply point to how your background situates you to achieve your goals. Naming a faculty member is important in some, but not all cases. More so in the EU (and UK) than in the US. 

But, the research area is important as a decision making issue in so much as there are faculty resources (including any named advisor) to support that area. If there are more resources in one area than in another, then candidates in the one with more is likely to be favored, at least a bit. So a school that doesn't do much serious work in AI, say, will probably look for candidates in other areas. This is especially true at the MS level, but also at the doctoral level. 

For faculty hiring, on the other hand, different rules may certainly apply.