For sure. I think that's sort of the disconnect in a thread asking about tactics. In such cases, I think instinct takes over, and I think it's usually going to be correct. Some 250lb-er hurtling out of control down a mountain? Yeah, you get out of the way. A little kid who you might be able to snatch? Yeah, you try. Every case will be different.
I think that's it. You make a quick judgement call and react. I have done it over the years with small kids. When our daughter was almost four she was a pretty decent tot on skis. She was starting to ski parallel, but would revert to the wedge in tougher stuff. We were skiing with her on a trail that's always groomed, and has a decent pitch. Later in the afternoon. We accessed the lower two-thirds via a traverse through the woods. Done it with her a ton, and she loved that adventure.
We THOUGHT we'd talk to her as we exited the woods and stopped on the trail. Nope. She just took off. Trail was all skied off and rock hard. She made an attempt at a turn or two, then got into the comfy wedge, and was going right down the fall line. Wedge got wider, and butt lower. Pretty soon no skis on snow, sliding on her butt and back. I guess the edges were creating some friction.
I guess I saw this unfolding. I don't recall it. I do recall making a few huge SG size turns and swoopping in to stop and quickly catch her. She was tiny. No impact. Pretty easy. Then of course as I caught my breath we turned it into what a fun slide, and how to stop. Let's get a hot chocolate. And agreed to be smarter parents. My wife was not pleased. We have plenty of experience to know better, and she is our youngest. Basically having any kid that age on that trail with those conditions was dumb.
Years later, about a year after a family friend had been paralyzed in a fall, hitting a lift tower, I was on a pretty steep trial, also just buffed, and I saw a guy in a free fall slide. Not doing a thing to slow it, no poles, no trying to roll to get an edge or boot buckle to dig in. Nothing. I think I wondered if he was knocked out. I quickly saw his path headed right toward a lift tower and a huge concrete pad. "Padded", but not great. So I did the same thing. I don't remember a thing, really. My wife says I timed it to ski right into him across the fall line, kept my skis under me, kind of flopped onto him and hugged him, and my momentum, I guess steered us quite away across the hill as we stopped.
I was really amped up, and scared afterwards. This guy was terrified. Had NEVER been taught how to self arrest in a fall, and was in over his head. His friends had encouraged him that he would be fine on this trail, "as it doesn't have bumps." Bumps would have immediately slowed hIm. Somebody had called patrol, and I guess they helped after that. I was very lucky not to have been injured myself. If I hadn't done the quick calculus of the tower, and I guess processed the slide, I would probably have let him slide until he stopped. No harm unless there is impact.
A few years ago we saw a guy in a long slide out West. We were far above him. Very wide terrain, nothing to hit. We watched him slide maybe 500 ft before he stopped, and he was sliding long before that. We skied by him; had a bunch of people with him. Looked like he was fine. I'd assume over his head. No fresh snow in over two weeks.
I don't know what I would do now, at 60+ in a similar situation. Hope I never have to find out. I think I would absoluteky swoop in to catch any child. Big guy....not so sure. Probably not. Hope somebody else younger might.
But yeah...no tactics to be learned in this.