I hope you ok'd this with your sister.
Yeah the you leash your dog why not your kid doesn't work for me either. It is exactly BECAUSE I leash my dog that I wouldn't leash my child. They simply remind me of an item for an animal and my children are not animals (most of the times).
Also there is very little chance my children will run off and bite someone ~ while the possibility that my dog might is only slightly hirer ~ they won't make me put my kid down if she HAPPENS to (not that I think my child or my goldendoodle would ever bite someone).
And yes I do allow my child to play in the unfenced backyard by herself ~ because I watch her. I don't have to stay out there every second because she knows her limits.
We rarely ever strapped the stroller straps because my DD1 didn't need it. DD2 hated it.
They only "strapping" we do of our children is in the carseat ~ and IMHO that is the same as a seatlbelt which I wear myself.
I don't do anything to my children I would want done to myself.
AGAIN JMHO! Everyone has one. I don't judge you if you put a leash on your kid. But lots of reasons people have given don't hold with me either. Of course if I see you I don't know your reason so I don't judge.
Do what YOU are comfortable doing.