Even 30 years ago when I first starting teaching, missing a few minutes recess, standing on the playground was about the only punishment allowed.
As the teacher I stood out on the playground for 20 minutes with the kids in the hot sun, too. I was in heels, pantyhose and school policy deemed teachers had to wear jackets with pants or dresses so even hotter than for the kids in shorts. Was that punishment too harsh on me, too?
Kids have to learn if you disrupt the class, you suffer the consequences. If you don't like the consequence than quit doing the behavior getting you there.
Also seems like the original poster's son was having trouble with his asthma . Sometimes running and exercise can bring on the asthma, so are you sure it was the standing for 10 minutes or was it the running around playing in the hot sun for the rest of recess that caused him to feel effects of his asthma? Does he have an inhaler at school? Or could it be one of the girls sprayed cologne or hair spray when they got back to class or the teachers perfume or something else in the classroom causing a reaction. Or could it even be stress of worrying about reaction at home when parent's find out you are misbehaving at school? Shoot, when my oldest was in first grade and I was home with the toddler, he worried that he was missing out at home and that his brother was doing things that he was missing cause he was stuck in school. He would tell me he was sick some days just to try to stay home. and there was the time he came in to our bedroom at 2 AM feeling guilty and not being able to sleep cause the teacher sent him home with a note for me. He thought it was about him pushing someone, but it was about volunteering. LOL There could be a million reasons for him feeling bad after a day at school.
BTW most school districts do not allow trees on playgrounds because of a safety issue of falling limbs etc. I remember when they came in and cut down all the trees at my son's school here in Florida.