Even though the admissions authorities now have to consider each case individually, in reality it means very little difference from before - it's just written out that they have to consider, doesn't mean that they have to agree to it anymore than they did before. Wanting to delay entry into YR is unlikely to be granted without significant evidence that the children has special needs that could not be accommodated within their peer-group.
Thinking that your child seems too young for school is unlikely to be one that a council would consider exceptional enough to allow a child to start reception a year later, especially if the child was also an Autumn birthday and had no specific SEN.
There is also no guarantee that they will be able to do the same at secondary and moving out of year at that point isn't a good thing at all.
I can see the very valid argument for delayed Reception entry for children with summer birthdays who are very immature, or who are prem and should be in the year above, or who have significant learning issues, and it's a really big dilemma for parents.
But, I think the situation in parts of the USA show some of the possible results of allowing free parental choice as to when a child starts school where you end up with a class of 4 year old girls and 6 year old boys as people red-shirt.
I have a lot of friends in the US with kids of the same age as my DD and every year there is angst and discussions about whether they should redshirt their sons because everyone else is doing it.
In the case of the OP, if her DD started Reception a year late, she would be nearly 2 years older than the youngest child in the class. There is enough anxiety for parents of summer-borns (I am one, so perhaps I'm biased) sending their just 4 year-old off to school with children nearly 12 months older let alone the thought that some of the class are about to turn 6.
The hope is that now summer-borns can start school in the first term of YR rather than later in the year, that this will show a big improvement in outcomes for summer-born children in the future.
Someone always has to be the youngest/oldest, but without really substantial and valid reasons, I don't think it is in the interest of the vast majority of children - which is what governments have to think about when they make these decisions.
In terms of the individual child, the parents do have the choice of looking at private education or HE if it is that important to them and they don't fulfil the criteria set by the LA.