In that instance, ride hailing solves that problem by being point-to-point. It also means you're not sinking a significant sum of money into the ownership and maintenance of a car if you're only using it a couple of times a week, e.g.: for shopping and maybe going out somewhere on the weekend.
That is only one of the points of public transit. Another couple points is to provide services to people who can't afford cars or have special needs (paratransit) or who can't drive (children and seniors)
Public transit in many parts of the country (not big cities) has very little to do with reducing congestion.
There are other complaints you can make about private shuttles, such as their redundancy, exclusivity, and the fact that they don't need a subsidy, but saying they don't reduce congestion, isn't one.
[0] http://nymag.com/daily/intelligencer/2012/12/silicon-valleys...
It can only reduce congestion if multiple passengers on different trips are in the car at the same time.
Not _only_: in the general case, there's nothing stopping taxi services from providing a last-mile (or rather last-n-miles) connection to transit compared to a car trip for the entire time. Depending on the way this works out, congestion can be reduced with private taxi rides. In fact, Beverly Hills city council passed a resolution to investigate driverless shuttles for exactly this purpose and precisely to reduce congestion.
On a personal note, I don't really understand what you're saying. Congestion goes up because there are less vehicles on the road? It sounds like you're trying to play contrarian and arguing for unintended effects and trying to assert something about short trips, but I'm at a loss for how your hypothesis is supposed to work.
The point of public transit is to reduce congestion. Private shuttles don't do this, so why should they get a public subsidy?