Why is it that when there is no Avel leading the services we often have different people doing it. We change the Baal Tefila for Barchu etc. Why don’t we say since one is already davening let him continue and finish?

Remah (O.H. 581: 1) mentions that in some places the one that recited Selichos during the Elul days, continues to lead the rest of the Tefilos during that day. Kol Bo (65) quotes that is is due to the principle of “Hamaschil Bemitzva Omrim Lo Gemor, “If one starts to perform a Mitzvah, we say to him, ‘carry it out to the end’ (Midrash Tanchuma Eikev, Yerushalmi Pesochim 10: 5). Indeed, Nezirus Shimshon (O.H. ibid.) questions why is that not the common minhag during the rest of the year and the Tefila is divided by others. Binyan Shlomo (Hacohen 36) explains that since the Tefilos stand in place of the Korbanos, we follow the traditions of the Beis Hamikdash where everyone sacrificed his own Korban. In that case, the many contributing their numerous sacrifices, takes precedence and we follow the principle of “Berov Am Hadrass Melech” or the honor of the King is when many take part.