Go on and tell us why, then.
For starters, the plan relies on a good few assumptions that are just ridiculous. For instance:
"Enough car-share cars would be made available that everyone could have access to one whenever they wanted."
"the system would ensure that a car was available to them when they wanted it"
That's one hell of a premise. But then it gets worse, when the sheer logistical nonsense of the proposal is detailed:
"For people who live out in the sticks, they would pick the car up at the public transport hub, drive it back home, and back to a hub (or anywhere they fancied) the next time they went out."
How are they going to pick up the car? Young mother of 2 Mrs Mcginty lives in the highlands. She wants a car because it's winter and she needs to take her youngest to Brig O Doon health practice because of his nasty cough. Are you proposing she cycles across to her nearest hub, picks up car, goes back, gets children, goes to appointment, drops the kids back home, drops car off to hub, then cycles back through the snow?
What's worst of all though is that this is a ridiculously elaborate scheme that will work in the most clumsy of manners, all to achieve something pretty simple.
The simplest way to cut down on private use of cars is just to put duty on petrol. It encourages people to use a car as little as possible. It encourages manufacturers to build more efficient vehicles. Ringfence part of the revenue and put it back into nationalised transport systems, and you get a positive spiral. Simple as fuck, achieves the behaviour you want, still flexible enough to accomodate the varied needs people have.