Sporting memories: you need to train like crazy
When I was younger my parents encouraged their kids to get involved in as many sports as possible. Looking back, I kind of think that a lot of this motivation might have been that there were 4 of us, and if we were all at home we would slowly drive my mother to madness but they also wanted us to succeed in life, and sports are a good way of making that happen because of the social aspect of it, the dedication it takes to succeed, and it gives a child confidence when they manage to consistently do well at something that they had to work for in order to achieve.

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Something looking like the above was a very common sight in my days when I was a kid and just because it was winter and there was snow all over the place didn't mean that I got to skip out on it. The thing was, I didn't want to skip out on it for the most part, I loved football/soccer and because I started to perform better at it than most other kids at a young age, I felt and even stronger urge to get even better. One image that stands out in my memory is me practicing corner kicks over and over again with something like 12 balls, until I was reliably able to bend it into the goal without anyone else touching it. It would be because of my ability to do that which would be instrumental in me getting a division-1 athletic scholarship to college because even though I didn't know he was there, I scored a goal like this, as well as 2 other goals in the same game, when a college scout was in the audience.
But it wasn't an easy road getting to that point
Just like all other kids I started out kicking the ball with my toes and just gathering around the ball and kicking in a way that didn't really accomplish much. We called it "bunching up" and it is quite difficult to train out of a kid.

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Anyone that plays the sport knows that there is no good reason for a team to ever be all in one place like this unless they must such as in a corner-kick situation. There is no benefit. It takes years to teach the kids that being spaced out and utilizing passing to open space is actually going to help them as well as the rest of the team. Just like anyone else at that age, I wanted the ball and I wanted it right now. In the mind of a child, the quickest method of getting what they want is to run over to it immediately and take it.
I think part of the reason why I ended up being good was because I had a good coach when I was something like 7 or 8 years old that offered candy incentives for those of us that managed to play the game in a non bunched up state for long periods of time in a row. Initially we did it in the hopes of getting a bite-size Snickers but eventually we started to see that we were winning most of our games specifically because we did this. We always had an open player while the other teams just had a pack of idiots that were constantly running towards the ball no matter where it was.
Later on in life once ability was recognized, I started attending training camps that had no team objective, they were simply for building of skills. I would imagine that my parents had to pay for these because they had real coaches, not volunteers, that would host them. On another occasion I got to go and train with the local college players on the weekends. They were no doubt paid for this as well but I learned a lot at those things because I wanted to emulate the taller, older, extremely talented players that I saw there. I really wanted to be like them and little did I know at the time, but I would end up getting into a much more prestigious school than they were attending at the time. I wonder if any of them ever knew that? Probably not.
I look back on the level of dedication that I had at that time and seriously have to thank my parents; There is no such thing as a 10 year old that is going to put that much work in on their own accord. I think back on how much my parents did to make that happen for me and am eternally grateful. Not only did my father have a full-time job, volunteered at various community things, but he also had his own sports that he participated in such as running and racquetball. How did he ever find the time just to drive us to all of these things and then, even build me a soccer goal complete with a net, right in our own backyard?
In all of my youth I recall spending quite a lot of time training for soccer and my dedication to it was steadfast. I honestly thin that there is some part that genetics play into it because I was naturally the right size for the sport, but without the training a person isn't just going to naturally know how to do footwork and how to kick the ball in the various ways that you have to in order to do well at this particular sport.
I put a ton of work in and must have been in seriously amazing shape to just run and run and run without ever seeming to gas out. I look back on those days with a sense of awe because I truly enjoyed it as well. I think I would be a far more successful adult if I were to somehow harness just a fraction of the motivation that I had back then and this is something that I fear isn't very present in the youth of today. I don't hear about any of my friends' kids doing anything even remotely similar to this. I presume there are some out there and maybe some of them are your kids. I know I certainly hope so.
This is not that common today with kids being able to play so many sports and it is slowly being lost due to parents having such busy lives. I can recall playing tons of sports growing up whether it was tennis, football, cricket, swimming or rugby and this was not down to my parents, but me as a kid growing up joining my friends playing sport. I have noticed most school facilities are closed over the weekends and school holidays which was our play ground and this has taken away something special we had experienced. Kids back in the day had computer games, but if it was a choice playing a sport outside or a computer game sports would always win.
I have no kids so I wasn't really sure about this but I think we can just look around and realize that what you are saying is true. When I was a kid we would go and look for pick up games with strangers and it would be fine, today those aren't likely to exist. Screens exist and this is where most people, including young people, are likely to spend their time. They are victims of their environment. When I was young there were videogames and screens as well, but we couldn't just play or watch anything we wanted any time that we wanted. This encouraged us to get out there and do something more interesting. I don't think at any point in my sporting career that being in good shape was ever even a consideration of mine. I just enjoyed playing a lot.
I was exactly the same as you always active and therefore was always very fit. Playing sport or sitting in front of a screen was always going to be sport as the winner.