I am always startled by the idea that anyone would attempt anything "figure skating" related on a public ice session ... which is an interesting "cultural norm". Coaches do not coach on public ice; figure skaters do not practice; it is just there for - leisure skating - which means, basically, skating around in circles,
The Canadian system seems unnecessarily restrictive to me. When we were going on a trip to Canada a couple of years back we were going to take our skates, but after doing a bit of research decided that all the requirements made the idea of skating during our holiday just too difficult. It seems to be aimed at preventing anyone but the most dedicated from skating, which is a shame. But as aussieskater said, it's just a different 'cultural norm'.
When we were living in the UK I always had my private lessons on public sessions, albeit on quiet (usually) weekday morning ones. It would have been pointless for me to have a lesson on patch (freestyle), as I'd just have been in the way. And as others have experienced, I wasn't allowed on patch until I'd reached a certain level (nothing really advanced, just basic turns, back crossovers, bunny hops - but these had to be practiced on public sessions), and even then only on certain patch sessions, as they were divided by level - which was a problem for me because the free for all sessions were during working hours.
Now that I do have lessons on figure skating ice, I'm not entirely convinced I wouldn't be better off on public sessions, as I would probably feel less intimidated, as I'm not at a level where I can get away with being assertive about getting done what I need to do, even in a lesson, which means I give way to everyone and have to only practice things that can be confined to a very small area. I should add that the figure skating sessions at our rink aren't divided by level, so it's everyone from beginner through to people jumping, spinning, and doing dance and pairs. Of course, I can't get to the quieter public sessions during the day (even though I can almost wave to aussieskater at her rink from where I now work), so the question is academic.
But to return to the original poster's point, yes, I used to hate having quiet public sessions ruined by the appearance of school groups, particularly when they'd cone off part of the rink for broom ball as well. It's very frustrating. It used to be okay if they were all wall huggers, as I could then use the middle of the rink, but when they're throwing themselves across the width of the rink, usually flailing, that makes things more difficult. I did once just pay my coach and refuse to have a lesson under those circumstances, as I knew it would have been a waste of both our times.