I remember the girls always walking the track while the boys had to participate in whatever the planned unit was.

Sort of, there were only enough for one class. Boys & girls ran separately, but at the same time. We only got them if the girls weren’t using them.

From primary school, we would have people pick teams one at a time. So yeah, you would remember who was in your team. I think the most numerous game would be football, but that would rarely be eleven a side. I ain’t saying I’d remember everyone’s name, but yeah, you generally remember the people on your side.
It helps that people are generally running in the same direction, or trying to attack you, you know? Faking being on the same team so you’d get passed the ball… never happened, in my experience.
By mistake, sometimes, but you’d have so many of your team mates shout at you for the mistake that you’d not do it again, haha!

Like I said, I’m really baffled this isn’t the norm. Maybe it’s a Gen X thing?
But that makes no sense. Younger generations are supposed to be more sociable, with much larger pools of “friends”. So surely it should be even easier for ye.