You are right, the toilets are not disabled - the users are.
Accessible toilets are intended for people who need the adaptations - the support rails, the extra space for a wheelchair, the positioning of washbasins, the space and privacy to change colostomy bags etc.
Some people will always need these adaptations, and the accessible toilet is the only one they can use. Some people, as you say, need extra support and space temporarily, e.g. if they have a broken leg.
Some disabled people need the adaptations on bad days, when their mobility or balance is particularly bad; on good days they can, should and do use the standard toilets.
The accessible toilets are for people who actually need the adaptations in them, who cannot use any other toilet and who have no choice but to use them.
Looking at some of your examples:
'A parent with a pram' should not use the accessible toilet.
Wider 'ambulant' cubicles are provided in single sex toilets, they have more space and some supports for people who need a bit of extra space or support, but do not need all the adaptations of an accessible toilet.
That's where parents with a pram should go.
They do not need the adaptations in an accessible toilet.
'A parent with opposite sex child' should not use the accessible toilet.
A mother can bring a young boy into the women's toilet. A father can safely let a young girl go into the women's toilet on her own and wait outside, often asking a woman to take her in and keep an eye on her -- that's what my father used to do when I was little
They do not need the adaptations in an accessible toilet.
'Being a trans person would count as an accessibility need' 'an accessibility need' means physically needing the adaptations in the accessible toilet, not choosing not to use all the other available toilets.
They do not need the adaptations in an accessible toilet.
Accessible toilets were campaigned for for decades by people with disabilities, for people with disabilities, who use them not because they prefer them, or they feel more comfortable using them, but because they need them.
There are no toilet police to keep men out of women's toilets, it has to work on trust and respect.
There are no toilet police to keep able-bodied people from using accessible toilets, it also has to work on trust and respect.