You don’t need cars if you’ve got good public transport networks.

Good public transport will greatly reduce need to drive and poorer/younger people will opt to not buy cars yet. But even in places with stellar PT wealthier and older people have cars, because they're always gonna be far more convenient in some situations. For instance, maybe you don't want to change between buses over and over. Or maybe your knees hurt and don't want to be standing up in a crowded bus/subway. Or maybe you are a woman and you want to avoid getting sexually harassed by creeps. Or maybe the weather is shite and don't want to be outside waiting for buses. Or maybe you want to go somewhere outside the city. People here sometimes overestimate PT and think it is a silver bullet where if PT is good enough then no one will want to have a car any more. That is not the case, it's just that they will use them far less, and specific groups of people will opt to not buy them, but it's not gonna be many of the people who are comfortable or above.

Small and narrow individual gardens are ugly and claustrophobic; a large communal ‘village green’ would be prettier.

No they're not. Small gardens are fine. People want their privacy. They're not comfortable with neighbours being able to see every side of your house and yard.