Why would they get in trouble for doing things like small shows, like what is the reasoning for it
So this is related to the notion of “professional” and “amateur” sports at the Olympics. Once upon a time, Olympic sports were all amateur. You couldn’t be paid for your sport. If you were, even once, no more Olympics for you.
Eventually, of course, the IOC realised this was getting a bit backwards, with the rise of professional sports and a lot of the “best” entrants in different sports being unable to compete at the Olympics. So the IOC gave the power to each sport to decided if it would allow professional or amateur athletes to compete. The ISU, as we now know, chose the “amateur” route (though they talk in terms of “eligible” and “not eligible” because the line has blurred a bit.
But what this means is that any event which a skater participates in - especially when they receive money for it - needs to have the proper approvals. For example, this past winter, I skated in several small shows. In order for me to retain my own eligibility - which allows me to compete domestically and potentially at Adult Nationals - our payments had to be processed through our state skating federation, which also sanctioned the events so that none of the skaters lost their eligibility. The payment wasn’t huge, but it was still a payment. If I hadn’t followed the proper channels for that, I could have lost my eligibility and not been allowed to compete any more.