I think PE should be mandatory. This is the case in my school district, and I think it's worked great.
First of all, I want to point out that those with a long-term injury (like a very bad broken leg), those who take a sport outside of school for a ridiculous amount of time (about an hour every day; mostly this only applies to hardcore gymnastics athletes), and those with a long-term medical condition that would PE kind of pointless (ie confined to a wheelchair counts, have asthma does not) do not have to take it.
Starting in elementary school, all kids have a PE class for one hour two days of the week, in the same way that they have a music class, computer lab, and science lab for an hour one day of the week. This helps kids who don't run around at recess have at least some level of fitness. In my school, the forth and fifth graders would run timed miles very occasionally (less than once a month), but no one cared if you took 13+ minutes to finish.
In junior high/middle school, all kids take PE (except for the aforementioned exceptions) as one of their year-long classes every year. In this class, they do try to push you, but not to the extent that they would get sued. Note that this is coming from someone who runs at the same speed as the asthmatics. Yes, the whole changing-in-the-locker-room thing is uncomfortable, but not unbearable. (This is coming from someone who flinches everything they are touched.)
In high school, because the number of classes you can take per year is less than in middle school, PE is only required to be taken year-long for two years. However, some of my school's sports teams require that their athletes take PE off-season.
Mandatory PE is great for kids with ADHD I believe, or for those who just want to let off some steam. After all, there's no recess after elementary school.
TL;DR Mandatory PE works great for my school district and I don't see why others would choose not to adopt it (the cost in implementing it aside).