There's https://www.car2go.com which ran for a year or so in my city but has since shut down. You could leave the car within the bounds of the city.
There are also various bike schemes with a similar idea?
I suspect that with all the VC money subsidizing Uber et al, for most people the gap between regular rentals for a day+ and just calling an Uber isn't large.
* cars are littered throughout the city rather than in designated parking spots
* cars are rented by the minute rather than by the hour
* cars don't have to be returned to where you got them from
The last point is the game changer. Now, it's feasible to do things like drive to the bar, but get a taxi back, or go on a long walk and grab a car back home when you're tired out.