At least in my city we don't need to go from 100 cars -> 1 train to solve the issue. Going from 3 solo drivers -> 1 Uber/Lyft will cut congestion to 1/3-1/2. That's enough to alleviate the worst traffic.
>Uber and Lyft are also not economical for a lot of people which is one of the other big reasons you don't see them taking off in many places.
The shared services are pretty comparable to what public transport costs in my city. A single bus/train trip costs ~$5 when taking all taxes/fares into account. Most journeys from point A to B require a transfer so the cost is more like $10. $10 in a Uber/Lyft shared ride gets you pretty far.
Even if it nets out to be more expensive it's at least something that people will use. The current riders are mostly those too poor to own a car and have no other choice.