And that is awesome! We loved sports as well and our kids played on our school and small town community teams. But like you we were also realistic. Just like band or 4-H etc, sports can be a great part of childhood development, learning and fun...however, when whatever activity starts stealing away that time and enjoyment, then it becomes damaging to the kid and family.
This is a key point. It also depends on sport. When I see people look at a football player that also plays other sports, that really isn't making the point. Value of training beyond strength and speed training in the offseason is pretty minimal, and the strength/speed stuff is happening with other sports as well. QBs are a different story, and sure there are 7 on 7 camps and all that, but going and playing another sport is as good or better. It just isn't a sport that requires incredible amounts of time building really specific skills.
The problem is the skill sports like basketball and baseball at a large school. If a kid wants to actually play in those sports at a 4A school, good luck. On those teams you might have like one rotation basketball guy that doesn't play club basketball but can still get on the court because he's just a stud athlete. Baseball maybe you've got a couple guys playing that aren't playing club ball on the decent HS teams.
I'll echo others that say do the parent-led volunteer approach and work with schools and cities to get practice locations. If you are in central Iowa, Des Moines is absolutely a hub of youth sports tournaments, and town, parent-led teams can absolutely participate. My kids did that type of route, and I coached until they were in HS. Once in HS, my kids did 3 years of the expensive clubs. They also did multiple sports through at least 8th grade, but ultimately went to one sport.
I will say that in both cases, the club coaches and experiences were great. My oldest didn't play in college as she had injury problems. But it was the club coaches that stayed in contact, came to graduation, checked in after surgery, not the HS coaches. My youngest is going to play in college and it was the club coaches reaching out to colleges, providing videos and information, writing letters of recommendation, etc. not the HS coaches.
I would love for things to be like the days before when a kid could play multiple sports, have plenty of opportunities through school and town organizations, and still get on the field/court. That's not the case at a lot of schools anymore. The risks and problems highlighted in the story are real. But if the answer is to just not do these clubs, then the chances that a kid gets to actually participate and play in some sports at a lot of schools is minimal.
My advice is to do the parent and volunteer led approach as long as you can. Then I'd say if multiple sports are not viable due to time commitments, then encouraging other clubs or activities that are not sports. Things other than sports are a little easier to co-exist with a heavy sports schedule vs. another physically taxing, high intensity and heavily scheduled activity.