Exactly. Improve the quality of public transportation and the usage levels of Uber and Lyft will decline. Whatever the failings of Uber and Lyft, and there are many, they can't be used as a justification to curb their use (essentially eliminate competition) so public transportation systems can continue their unchallenged mediocrity.
When the wealthy are forced to use public services, all of a sudden, they become interested and politically engaged in improving them.
Uber doesn't drive improvements in transit in this sense - it starves it of political capital.
The best transit services are ones which are used by a wide swathe of the public.
[1] If you are regularly paying $6-30 for a one-way taxi commute, you are either wealthy, really money-foolish, or a truly special case.
Costs me $0/day to take the bus or light rail, subsidized by my workplace. $3-$4 if your workplace doesn't subsidize and you get a regional pass.
Ride-hailing services don't have this particular problem. They only need to serve based on rider demand. Yet at this moment they do rely on subsidies by VC money.
When I'm in Tokyo I don't use Uber because the train system is so clean, fast, and safe; I have no incentive to use an Uber.
When I'm in places with slow buses that get stuck in traffic, or operate trains with disgusting facilities, I'm more likely to choose Uber.