So, in theory, as long as the frequency is high, the low value will be compensated. In practice, the problem is the specific ways in which liquidity can be built. In your example of car sharing, the supplier/driver has very little incentive to begin with. The driver also does not know how high the frequency can get with such low transactions. Combined, these two factors make it very difficult to ensure enough liquidity in the marketplace to spur demand.
Another thing to think through is the time it takes to complete a transaction, particularly true for service-oriented marketplaces. All things being equal, the faster the ride ends is better for both the rider and the driver, but if the transaction value is low and the time/ride is high, then that eats up the value in the marketplace as well. In this case, Uber was very lucky that most of these factors worked out for them. See https://twitter.com/davidsacks/status/475073311383105536?lang=en which explains the utilization beautifully and how lowering prices can work for drivers and riders both. Based on this, one can argue that your example will work too, and maybe it will. The thing to keep in mind is whether the size of transaction is large enough to make it worthwhile for the drivers to come into the system.
In case of AirBnb, for example, the supply side is pretty fixed. The unit of rental is one night, so there is an incentive for the supplier to raise prices, which is in opposition to the consumer, who wants cheaper rents.
Also remember that in such marketplaces, the suppliers tend to be professionals, i.e. they rely on the marketplace for their primary income. In this case, I would say that the roadblock is not so much for the ‘sharing’ economy, but rather for the ‘gig’ economy, where a lot of people are opting for these gigs as their primary source of income in return for the flexibility and freedom it provides.