I've seen this work in the States, and it works very well!
To answer a few of the issues raised...
Insurance: In the US you insure the car not the driver, not sure how the system works in the UK, so the cost of insurance is built into the rental cost.
Parking: If a parking ticket is recieved at a certain time the system knows who had the car and debits it from the persons account
If you mean storage, yes, a problem but the same with opening a new shop etc. so up to the business to figure that one out.
Discipline: Any problems and again, you get charged. You pay by the hour so no set return time. If especially untidy, an additional fee is levied.
Dings or smashes: Again, on getting the membership card (which allows you access the cars [the system I saw was like a vending machine where you swiped your card (possibly some security checks, wasn't watching that close), choose your car, keys pop down and then you drive away]), they take full financial details and will charge you any excess etc. on the damage. Didn't look through any of the Ts&Cs, but I'm sure they'll charge fairly well if you damage the car. Again, more difficult in Ireland where the driver is insured not the car. You could organise it with only fully licenced drivers who have to anually show they have insurance cover to cover "driving other cars" to a comprehensive level.
The next person relying on the car: Would still have a fleet to select from (in the US, would Irish usage patterns allow for such high levels of stock??).
In the US, you can pick up the car at one depot and drop it off at another (so pay for 1 hour driving). Then stay near the second depot for the day and after drive home, different car possibly (again, only paying for 1 hour driving). So you can have a full day away with only being charged for 2 hours (I believe the large car rental companies here run this kind of thing, pick up at one outlet drop off at another).
Again, how many depots for these would be viable in Ireland? Just in Dublin? Multiple in Dublin and one in Cork and Galway? Etc...
Still some serious issues, but an idea I'd love to see come into play.