My children were born in the nineties. It was considered normal for a girl to be toilet trained around her second birthday and a boy by around 2 1/2. Some playgroups started at 2 1/2 and children had to be toilet trained before they started. My oldest son is autistic, but I didn't realise at the time. I was horrified that he was still in nappies until just before his third birthday, but he was immediately dry day and night. Once we realised that he had a serious problem, the late toilet training made sense. He had problems in the other direction until he was eight. My younger son and daughter were trained at roughly the expected times. Over on MN, it seems that three is the earliest many modern parents seem to consider starting potty training and four is common as they wait for "readiness." They wonder why their children are unwilling to co-operate, but three-year-olds can be very stubborn. It is easier, ironically, when they are younger. I do think laziness is involved in many cases. In the same way, so-called "gentle parenting" seems to mean no parenting. I do think that children should not be allowed to start nursery or school if they are not toilet trained - the odd accident is an entirely different matter - unless they have significant needs.
As for general parental responsibilities, I started school in September 1969. My mother has never forgotten the teacher standing at the school gates (parents were allowed no further) and telling them all that they didn't need to worry about teaching their children to read because that was her job. Their job was to make sure that their children could put on their shoes by themselves and button up their coats by themselves as she did not have time to button up forty coats. No classroom assistants in those days, of course. She was an excellent teacher - firm but fair and everyone knew exactly where they stood. I have very happy memories of my first year of school. My teacher, Mrs Scales, would be turning in her grave if she knew that children were turning up to school in nappies.