This isn't really how parenting works, though, is it?
Children (and parents) aren't robots and don't have set input:output responses.
Something might require force on one day on one incident, whereas every single other day it's perfectly fine and other ways to get the task done work fine.
A parent might have access to more patience, energy, creativity on one day, and another day they might just be done and say nope, let's go.
If I can think of some examples that have happened in my life where I've used force:
- Crossing road with toddler age child, holding hands. Child goes limp in the middle of the road and refuses to walk. I am holding something in other hand. I cannot scoop them up and put them on my hip. I have no choice but to pick them up by the arm and walk to the other side of the road.
- Baby/toddler (under 2) does not want to change clothing. Their clothing is wet, dirty, or inappropriate for the weather. Songs, games, distraction are not working on this occasion. I change their clothing as quickly as I can despite them crying and protesting. Then they are free to go off and play (or have bedtime milk or whatever they actually want to do).
- Child does not want to wash hair. I've already left it for as long as possible. It's now dirty, sticky and really needs to be washed before it gets matted.
- Child has hold of an item (e.g. a large, heavy stick from outside. A kitchen utensil. A paint roller they found in a drawer. A large, heavy book.) which can cause serious injury and is waving it around and being unsafe. Will not put it down when asked nicely.
- Child is hurting an animal or younger sibling and will not stop in response to verbal direction.
I could of course also solve all of those problems in other ways. I often now pick up a toddler child before crossing roads rather than expecting them to walk. Or teach them to cross safely and maybe don't make them hold hands (depending on age/likelihood of bolting). Or bring a buggy. But I didn't have any of these options on that one occasion.
I often employ distraction, songs, games, bringing a toy, getting toddler involved in getting dressed etc. But sometimes they are just too tired or ragey to cooperate. Sometimes you can wait until the rage passes. Sometimes it makes more sense to just dress them without waiting. Sometimes waiting will lead to them being more ragey, more tired etc and make the problem worse, so best all around to get it over with.
I used to wash DS1's hair with just a flannel, or just water (requiring fewer rinses than a method that needs to get all soap out). We had already cut it shorter to make washing less of an ordeal. After a while of waiting for this to get better we started a targeted program that I made up with different stages of comfort building up from having water poured over his back, to the back of his head, to the top of his head etc until we built up to full hair washing. He did well with this and we probably could have done it earlier but I kept thinking he would grow out of it, I'd never heard of a child needing to be trained/acclimatised to accept hair washing.
Sorry I got nothing for the removal of dangerous item from child's hand! Sometimes you just have to take it off them before they hurt themselves or somebody else. It's not always possible to have every possible thing kept up away in a childproof location. Children can make surprising items into a weapon if in the right (wrong) mood.
Likewise, sometimes you just need to remove them (or remove the younger child/animal) by picking them up and taking them away. And then sometimes holding onto them or putting them somewhere they can't get out of to stop them going straight back.
Nobody has perfect knowledge, foresight, patience etc. It's fine to say that you have never used force and try to avoid it wherever possible and research the perfect method etc as soon as you come across a slight issue, most people do not have this capacity, in fact I think you'd be hard pressed to find anybody who does! I think you must be overlooking times where you've suddenly been presented with a situation that needs action. Perhaps then you are an unusually effective person and have stored that incident for research in case it happens again in future, but most people wouldn't do this.