Yeos said: “The above should be understood as kusala kamma not having any influence upon rebirth?”
Yes. It does. Kusala kamma help one attain Nibbana, or stop the rebirth process, starting with rebirths in the four lowest realms at the Sotapanna stage.
– Punna kamma help with that too, since they help one avoid rebirths in the apayas: “Kusala and Akusala Kamma, Punna and Pāpa Kamma“.
Most of us cannot understand yet why one needs to stop rebirths in all realms. That does not need to be contemplated until one gets to the Anagami stage.