Why does the league system exist?

I'm talking about the wood/stone league thing in chess.com.
So basically: If I play way too many games, lose all my friends and become a hikikomori, I will get to emerald league and dry my tears with a worthless virtual trophy?
Do people fall for that? It's a typical EA/Activision move to get people addicted.

It's not even hard to get promoted. Playing 1 hour a day will get you the first few promotions easily.

Playing 1 hour a day in arenas would get you to elite or even champion league.

For example I see you were promoted out of wood for winning about 7 games... that's 1 game a day on average. Hardly an addiction or time consuming.

Simple gamification that exist in almost any modern mobile or non-mobile game or plattform, because it works. Once you get people hooked, they love to see the numbers go up and compete with others without actually having to do any heavy lifting (get higher ranking and win tournament). After a while, most probably quit. Some will ignore it forever while other probably return for another sprint. 

Little bit like keeping up winning streaks or attendance streaks in other apps.

Well I hate it. Same with the attendance streaks. That's why I disable notifications on every app.
It's an attempt of a corporation to take over my life. It's none of their damn business how often I use their service. And since it doesn't involve heavy lifting, as you put it, that also means it's worthless.

People like to see progress. It's provides a distraction from the status anxiety of your actual rating.

How is playing more games progress?

Well, I ignored chess league here but I like it on duolingo. Simple gamification which work as an extra motivation to do just minimal amount even on the days when I really don't feel like doing any language at all. Pointless and could harm the actual enjoyment or learning if one chase some imaginary score instead of learning and playing chess or the language on chosen, but as a small nudge it can be good.

If you play chess for fun, you could see it as a measure of how much fun you're having. If you hate chess then you could see it as a measure of your progress as a masochist.

I don't need to prove my masochism. I beat every dark souls.

Quality > Quantity. I prefer eating one good stake, instead of a whole buffé of cheap cuts.

Forcing people to do things. What's next? Chessturbate?

I don't actually know why that thing exist but I am not in any league anyway so.. 

You can easily leave the league if you don't like it I don't know why anyone would have a problem with it though.

You can go to the league page and click Leave League and you won't participate.

Because some people will get stuck in it, just like microtransactions and lootboxes in games. Most people can ignore it, for a while at least, but some will do something harmful even when they know it's bad for them. "Just one more spin", "just one more game", "just win back my money and quit". 

At least league don't cost money and only possible negative outcome is an unhealthy amount of time spent on chess while chasing first place. 

leagues are unhealthy for people, but unfortunately they decided to add league achievements in right before i finished unlocking them all, so i was too invested to not participate:

at least the frenzy has died down somewhat & i'm leading my elite division without too much effort.

I guess that it maybe makes people to play chess a little bit more but is it bad or good thing? Some people needs motivation to it would be fun for them and having fun is the point, isn't it? As far as there are not involved any money, payments and etc. I don't see a problem. If it was bad only because its a competitive thing then every competitive sport would be bad. 
I personally don't see much sence in this feature and I am not in any league but maybe some other people like that. Comparing it with microtransactions feels a bit weird to me...

While I love gamification in general, at least when done for a good purpose (making medicine taste good is fine, making fast food taste better and potentially more addictive is less fine), this specific type of gamification or at least it's implementation is a bit iffy.

What are this type of league motivate people to do? It's not a "good learning" scoring where by doing one lesson a week, at least one puzzle every day and one game with review get you point. That would motivate new players to adopt somewhat good learning practice and not to drop chess for a long period of time. But leagues like this, both here and on duolingo, have a tendency to motivate "quantity over quality" grind. If you want to continue to advance find what gives you most points per time unit and then do it whole day. No time for lessons since they give 0 points, no time for puzzles since they are worth 0 points and no time for reviewing played games. And since you have an upper limit on number of point you can realistically get in an hour, you will have to increase amount of hours played instead to increase your points.

You see where it might get wrong for some people?