The mishna apparently does not give a reason that it explains the function of these two offices in particular. All the others are covered in other places in Shas; why did Rabi Yehuda Hanasi see fit to explain specifically these two here in Shekalim?
While I did not see anyone address this, I would say there are two connections to this chapter. The general connection is that the beginning of the chapter talked about the caretakers of Hekdesh whose main job was to deal with the donations to Hekdesh.
However, I believe the connection is also to the previous Mishnah which discusses a person who lost his Chosam and does not have money to bring other libations etc. The Mishnah says he can wait around and see if at the end of the day the money vs. amount of Chosams did not add up and showed that he deserves to receive them. This indicates a poor person. It is possible that the Mishnah is saying that a poor person who could not wait until the end of the day, or who unluckily had the money add up, had the option of taking money from the Lishkah in order to bring his libations anyway.
All the best,