It would seem then that on this thread there are two schools of thought: one to protect at all costs, nothing physical but perhaps less freedom; the other to allow more freedom the cost of which is a slightly firmer hand to reinforce the lessons. I don't see any problem with either way of doing it so long as kids are neither beaten nor kept so protected they cannot learn or enjoy the world. I imagine a lot depends on the upbringing of the parents and the nature of the children themselves.
I don't think I really fit into either school of thought tbh. I think freedom is essential for children and don't tend to wrap mine up in cotton wool, I discipline with a firm hand but I don't smack/spank. Neither do I use a playpen or a walker although due to the layout of my old home I used one gate for the kitchen which I used when I was cooking and baby was mobile (my eldest was on her feet walking before 9 months and I had a small narrow kitchen.)
I don't think that freedom has to be sacrificed in order to gently discipline a child tbh, although I think restricting freedom can be a tool to discipline as a child gets older and can understand the relationship between earning trust and being given increased freedom and independence.
I protect where necessary for the childs age and allow freedom where appropriate. If baby went to touch something uncovered, (especially when visiting as people with older or no children don't generally babyproof), then If I was close enough to physically reprimand a child I'd be close enough to get quickly down to their level and firmly redirect, guide or remove them with a simple fim instruction/warning word. Assuming the physical reprimand does not cause pain as has been said and is simply a shock tactic, then this would presumably have as much impact as a 'tap'. I know some people use 'owie' words to get the point across and as has been previously pointed out children are remarkable learners and can connect pain to objects quite early. This way though there is no confusion which could be argued may be involved when a parent smacks a hand (the argument being that the focus on the pain can in some children distract from the importance of the instruction.)
If out walking my kids liked to explore as much as the next child and were often without a restraint so that they could run ahead but if we were in a busy mall or near a main road then they would be in a sling, holding an adults hand or in a buggy/restraint until such time as they learned basic traffic/road sense. I found 'The traffic club' a great resource for this which is sent out by the govt when children here are 3, we started it earlier with dd2 because we had a copy of dd1s. It worked very well and dd2 was able to be trusted from a very young age while out and about.
I do think it is important to babyproof to some extent and supervise an infant who is too small to understand basic instructions. If a small infant hurts themselves badly because they were allowed unsupervised access to a dangerous environment then I think we would all ask where the parent was, not whether the baby should have known better. A baby who can't understand basic instructions or consequences is unlikely to understand a tap any more than any other consequence.
As children get older it's simply a question of which consequences or methods we choose, but I think if a child is old enough to understand a tap then they are old enough to understand other consequences.
I probably give my two more freedom than some people on this forum would think was appropriate, but I trust them and feel that they've learned the lessons that they need to be allowed that freedom. I also think that it's important that kids realise from early on that freedom is a priveledge as a child and a right as an adult which can and will be removed as this is the consequence that our society uses through their life for not behaving appropriately within it's rules. They learn very quickly that this freedom can be removed very easily if they don't follow the lessons that they've learned as they've grown. I think in fact my eldest would much prefer a smacked arse than any of the consequences that we have in place for misbehaviour, she values her independence and freedom too much to enjoy having any removed.
Still, although I disagree that there are two basic schools of thought ie: firm discipline and freedom to explore versus protection and gentle discipline I do agree with your conclusion.