I see your point Molehill. Myself and a friend have been sharing the school runs for a year or so now, with our ds's, I do Tuesdays and Wednesdays and she does Thursdays and Fridays, (mornings only, both boys have various clubs etc after school so we do our own thing then).
Thing is her ds is more of a handful than mine, he's calmed down a bit now but there was a time he'd just argue, want to go a different way, didn't want to carry his bag, wanted to run down alley way on his own and meet us at school, etc etc!
I had to get quite firm with him and tbh missed the 1 to 1 time with my my own child in the mornings. The other child has got a bit easier but since September I've said on a Monday I just take ds. He was also saying he wanted some time without the other boy. Obv if my friend couldn't take her ds for any reason the odd Monday I'd step in and vice versa.
He also says he can't "talk" to his friend's mum like he can me, so sometimes even when it's his turn to go with them he'll ask me to take him!
Sharing school runs works a treat sometimes, but doesn't suit everybody all the time! I think my friend was a bit put out about the Mondays tbh, she did say once or twice if she was going anyway why couldn't my ds just go with them, or vice versa. But then I don't get the feeling her and her ds are that bothered about time to themselves, she'd rather have other kids over for him to play with or have him at somebody's house pretty much all the time so he's occupied. We do a lot of that ourselves but also need time when it's just us as a family. Everyone's different I suppose.