The order of tefilla is that there should be praise, request, and thanks. It seems like this bracha returns to the idea of requesting so why is it at the end of the amidah where one would think brachas only relating to thanks should be?
See this article especially the explanation on page 2.
Essentially, it states according to one opinion "Sim Shalom" was a format for the individual to recite Birkat Kohanim - the Priestly blessing. This includes a request for peace. (See the article as the term "Birkat Kohanim" does not necessarily mean "duchenin" - the Kohanim saying the blessings from the Bimah. There were times during the day when they recited the blessing without the "duchan.)
The Siddur Tefillah Roke'ach 41 states that Sim Shalom was designed as a chazzan;s prayer to recite a request for peace after Birkat Kohanim. (Why Birkat Kohanim itself has a request for peace, is somewhat discussed in the article, incidentally.)
There is a general requirement that all Brachot and Shemoneh Esreh itself end with a request for peace.