They won't be healthy if their MH is wrecked by stress and they are generally miserable about being forced into stuff they do not like.
Sounds like he has yet to find sports he likes.
Yes, I think it's important to be active - doesn't have to be organised sport, but does need to be something that you are really doing (IYSWIM, as it's all to easy to kid yourself you are doing more than you really are if you don't have an imposed external structure)
Make sure he has exposure to plenty of sports (perhaps during holidays), try to get him along to something like Junior Parkrun (which is active but not remotely competitive, it's all about community and participation).
One of my DC did not find a sporting passion until the early teen years, at which point they started training seriously 2-3 times a week plus strength/conditioning sessione.
So yes, it can happen later. But I think your main focus right now should be on combating resistance before it becomes entrenched. So don't try to send him back to a sport he's tried but doesn't like at the moment. Do try new things.
And find out what non-sport things he wants to do too, and make sure he gets extra-curricular opportunities for those too.