If there is a change in shaliach tzibur, why does it occur at Yishtabach if yishtabach is the ending beracha for pesukei d’zimra? Why not have the change after the kaddish before Borechu which is a natural break?
Please include sources.
There is no point for one person to start Kaddish, and for another to take over for Barchu — though this is theoretically possible.
The person, where one is appointed, who says the Pesukei De-Zimra out loud, fulfills no purpose other than timing, and a child can also do it (see Aruch Hashulchan 53:1).
The Kaddish serves as a “partition” between one section of davening and another, and it is simplest that the Shaliach Tzibbur for Shacharis should start from there.