This issue is bashed out fairly frequently on here. I think there are a few 'givens' that need stating.
Everyone has the right to go to the toilet in privacy and with dignity.
This to me would mean not having to go to the toilet with the door open - you may need to change a sanitary product or something like that, and I wouldn't expect any woman to have to do that with the door open. Equally, it would mean a disabled person having a toilet available that was suited to their needs.
Everyone has the right to keep their children safe
Some people would be happy to leave their child in a buggy outside the cubicle. Some people would never dream of doing this. It's a personal decision. Rather like whether you're happy to leave a child in the car whilst paying for petrol.
Facilities should be available to meet differing needs
This might be the needs of a disabled person, or might be the needs of a parent with a child who needs changing. They are not mutually exclusive.
There are other issues besides being able to take a buggy into the toilet. As has been mentioned numerous times, the changing area is frequently sited in the disabled toilet. But it may also be in the ladies, which of course renders them unusable for a dad. What if you are a dad out with a toilet trained girl who is too young to go into a toilet by herself? He can't really take her into the gents, nor can he let her go into the ladies on her own. What should he do?
So my solution is to have;
Regular Ladies and Gents toilets
Dedicated disabled toilet with facilities for older children with disabilities as well as wheelchairs (as riven has described).
Unisex family rooms with toilets, and a changing area.
John Lewis seem to manage this. Shame it isn't more common place.