We had a client once whose baby got polycythemia. It got pretty serious, and a unilateral decision was made to clamp immediately with the next birth. The next baby didn't get it. I get clamping early if mom has a history of polycythemia.
Anecdotally I only know one person who has had a newborn with polycythemia. It was her third baby, first and second were fine. She went on to have two more babies and both of them were fine too. #1-4 were born in the hospital so I don't know how long their cords were left to pulse (including #3 who was also hospital born), #5 was homebirthed. I was present, and while I believe Mom would've waited longer for the cord to be cut if she'd been asked it was certainly left pulsing much longer than is standard in our local hospital.
Since polycythemia is a condition of the baby, not of Mom, would there really be a history of it based on whether or not same Mom is delivering another baby?
Also when I was doing some research on polycythemia all causes are lumped together it seems, with placental transfusion being only one of them. I'd be interested to see real research on how "dangerous" it is if baby "just" has their full blood volume transferred, with no other underlying issues.