I did a blog a while ago on Small Circles and how to teach it.
I think doing Small Circles is an important skill and rightly a required Junior maneuver, not so much for the circles, but for other things. However, as Nathan has pointed out in the blog comments, doing circles quickly is important in racing, if you're bad.
In Small Circles, there's a lot going on in a short amount of time, so it's a stress test of your sailing skills, your boat control, your weight balance, and your crew communication. Sailing a circle flawlessly (of whatever radius, but constant) is a challenge. One very good Club racer told me that one of the best racing exercise is doing lots of circles in a row, maybe 100.
But really tight circles is a different beast. It has all of the challenges above, but it requires some rudderless techniques to make the turns really fast and tight. My blog of a couple of years ago missed an important thing.
In the blog, I talked about how you do fast upwind and downwind turns, which to me is the real value of learning this. You might have to do either near the dock, combined with a tack or a gybe. But I glossed over the gybe itself, which is an important part of it.
So you're doing a fast downwind turn, mainsheet out and hiking out hard, and you're going into the gybe. First, you have to get your weight into the boat as it flattens so as not to capsize. Next, you keep the tiller over and keep turning through the gybe. You do not stop the turn.
When we learn gybes, we learn that the most important thing is to stop the turn after the gybe. If we don't we capsize. The reason is that sailboats lean to the outside of the turn. The faster we go, the more they lean. If we keep turning in a gybe, we'll lean over as we round up and capsize. So we learn the counter-steer to stop the turn. Any good Junior has this imprinted in their muscle memory.
But here it's different. If we're doing a really sharp turn downwind, our boat speed is very small, so if we keep turning, the boat won't lean very much, and we won't capsize. In fact, if we stop the turn, we increase the capsize risk when we turn upwind, as we've picked up speed going downwind.
When I teach it, I do the exercises I mentioned in the earlier blog, fast upwind turns and fast downwind turns. Then I have the student do a fast downwind turn and keep the tiller over through the gybe. They're usually reluctant,as it's counter to what they've learned so well, but they are surprised to see that it works. I think of this as breaking them of a very good habit.
Once they get that, they're on to the more difficult part of the small circles (upwind). But that's another topic.
I'll mention that there's some controversy about how tight the circles should be (Seamus Vanecko famously said that if you ask 10 skippers, you'll get 11 answers and a fist-fight, I'm sure about some other sailing issue, but it applies here). I teach tight circles because I think the skills you learn will help you in close-quarters situations. But I also recognize the value of just sailing constant radius circles, a lot of them.
And BTW, a lot of this applies to keelboats, and you will have to do circles occasionally, for example in the Marina to get out of the way of a procession of boats going the opposite direction. But that is also another topic.