Skinthin
Even on the shoe thing I think it's context dependent, which includes the child's age.
I'm not a huge Sarah Ockwell-Smith fan, and find it a bit middle class yummy mummy at times, but the one thing I took from a range of authoritative parenting resources was about being mindful over choosing boundaries and when to drop the rope.
I find it bizarre that an adult would get into a power struggle with a 2 year old over shoes, for example. If mine took their shoes off in the car and we were going to the doctor, I'd just lift them out the car and go to the appointment. No attention given to the behaviour, no drama, no need for conflict. I never felt the need to "win" or show them who's boss, which comes from a place of fear eg if I don't get into this unnecessary battle now I might have an 8 year old who is feral and won't wear shoes.
I struggle to put myself in the shoes of an adult who would pick a fight with a 2 year old over things that don't matter.
Once the adult gets themselves into the conflict it often becomes a power struggle and the adult is left either having to back down (which is sometimes needed because we can all be unreasonable at times) or it becomes a silly battle of wills over nothing so the parent can feel they've won. Too much backing down ends up being permissive because the child doesn't learn that there are consistent boundaries and the adult is more likely to keep letting everything drop for ease.
If they're 5 and we're walking to the hairdresser's then shoes aren't negotiable. They're a safety situation. They'd be free to choose which pair of shoes they wear, but shoes aren't negotiable. If they can't make the choice, I make the choice, hold the boundary and move on.