I have been learning a lot by seeing what differing opinions even we Mamas at Mothering have regarding playground etiquette. I guess when you consider how differently grown women see things, it stands to reason that when many of the people supervising the children at my local playground are mere children themselves, there are bound to be a lot of areas where I can't just assume that everyone will see a situation like I do.
When I think of older children's responsibility to be mindful of younger children, I think of examples like:
1) When you are clambering around on the equipment, you need to be patient with a slower-moving child in front of you; you don't go around her unless there's enough space to safely do so without knocking her off-balance.
2) When playing tag, if you suddenly see a small child in your path, go around her. Do everything you can to avoid crashing into her.
3) If you're sliding down the slide and notice a child playing at the bottom, stop yourself rather than landing on her.
4) Before climbing up the slide, look up to make sure no one else is trying to slide down (not that I've ever seen anyone get hurt from someone coming down while someone else was coming up, honestly, but some folks seem to see this as the ultimate in dangerous situations).
I think the rest of the playground area differs from the swing area in that the kids playing on the general playground are bound to periodically intersect with other kids' space. It's a shared playspace, whereas I think the child on the swing "has" the space that she is swinging in.
If others get hurt by a child on a swing, it's because they went into the swinging child's space. Sure, it's great if the child on the swing happens to notice that a collision is about to happen and is able to quickly do something to prevent it; I just don't think it's reasonable to hold a child immersed in the throes of "flying" to be on the alert for other children who might walk into her space.
I agree with laila2, ollyoxenfree and VisionaryMom who talked about the importance of teens being welcome in public spaces. I think this welcome should include older kids who still want to enjoy carefree pleasures like swinging with their eyes closed, even though they're past the "tiny" stage.
As far as only swinging with eyes closed if there's no one there, my kids actually enjoyed playing on a deserted playground when they were tiny. My 5yo would probably still enjoy this, but my 10yo only finds it interesting now at the "higher traffic" times.
So maybe the people who think they shouldn't have to supervise their little ones too closely around the swing area should choose the lower traffic times, since most 2 or 3yo children will be just as happy being the only child on the playground as they will be a in a crowd.
Of course, this doesn't work for little kids who have to wait for their older siblings to take them. Even though school is out for the summer so the older sibs could technically take them at 10 AM, I imagine the sibs also prefer going at the higher-traffic times. So it's just a case where we all have to live and learn.