Think of the congestion charge as a charge on the vehicle, rather than on the person, as the stated policy goal is to reduce the number of vehicles in the CBD, not the number of people overall. The Uber is very likely going to continue to be used to service other passengers after dropping you off within the same calendar day, so one potential "fair" solution is to split the congestion charge among the many passengers using that one vehicle. That is your reduced Uber toll charge. But even in this case, it's not really an even split, taxis are going to generate a much higher congestion charge revenue than a single passenger car.
The rideshare toll is already a charge on the vehicle and not the riders. If you share an Uber with two other people, the per-person congestion fee for the trip drops to $0.50.