What you are essentially asking for is to take duty away a parents discretion in blocking harmful people from their children’s lives.
Absolutely spot on. The very few 'good' grandparents out there, this law is for them, but it will be the toxic ones who will benefit from it. They do love a bit of control.
Grandparents had their time as parents. Grandchildren are not a do over and are certainly not the property of their relatives, even their parents.
This is very accurate. My parents consistently referred to MY son as 'theirs'. Kept comparing him to my brother. Kept saying I looked like the older sister 
It got to the point where they were taking him out without my permission, even tried to take him on holiday! They were furious that I wouldn't let him go. His response was 'what does it matter what we do with him on our watch? He's OUR grandchild'
She would say to my DS, 'I can't wait until you're a teen. I hope you put your mother through hell, like she did with me'.
You think I want these people to have access?
You think, that even though they fucked up my childhood, I should say. here ....have my kids....fuck them up as well?
Just because there is no physical abuse, it becomes very hard to prove. Anything I say, they could refute. As is it, they are already spreading lies about me, how I'm mentally unstable etc
My ex was violent, and financially abusive, emotionally abusive, extremely controlling. When I got away, he still had rights to see DS. Despite his drug taking, despite being an alcoholic. Despite drink driving. Despite his parents being abusive (his father raped both his sisters).
So, when a woman leaves her abusive ex, now not only would she have to deal with HIM having contact, but his parents too.
The world isn't full of poor old grannies, who have mean and nasty daughters deliberately 'punishing' them, just because.
There are damn good reasons for no contact, and they take YEARS to get there.
Esther always stuck me as a narcissistic grandparent anyway. Why else would she be campaigning? There was an article about her being a 'naughty granny' and how it was her right to be that 'naughty granny' and not do what her daughter asked of her. That to me says childish fucking narcissist. Like my own mother.
And then there's the Jimmy Saville thing. Like fuck she didn't know.