Active coaches cannot be judges. That's a lot more ripe for conflicts of interest.
(Also, there's the whole history of amateurism, which shaped the way the sport is structured but isn't directly relevant today.)
Pro competitions often used retired elite skaters currently coaching as judges. "Ineligible" persons all around!
Plenty of good skaters can also go on to become good coaches or good judges. If they want to stay involved in the sport, they generally choose one or the other depending on their interests and talents and whether they have another primary means of earning a living. Some coaches retire from coaching and become judges, or vice versa, though not usually at an international level.
Others may have been great at doing it themselves but not so good at analyzing or teaching. Some may have been mediocre at the physical skills themselves but are great at the mental skills.
Coaches see a limited number of skaters as their direct students. If they teach in a group setting or give a bunch of seminars they can work with more total skaters each day/month/year than if they only teach private lessons. If they teach lower level skaters who take fewer lessons, they may have more total students. They probably also see other skaters who train at the same rink with other coaches. They see a lot more skaters that they don't work with when they accompany their students to competitions. Some may be very objective about how their students stack up against the rest of the field and some may be very biased. Their job as coaches is to support their own students, so some bias is probably a good thing in a coach, as long as it doesn't blind them areas where their students could use improvement.
Judges who judge almost every week, from low-level local competitions (and tests in countries with test systems) up to national and international events, see a lot of different skaters at all levels. Judges who only judge a handful of competitions a year, especially events with few competitors (Grand Prix, for example), not so much.