I agree.
Now, we mostly see the demand for parking at zero [#] marginal cost to the parker, not the demand for parking at its true cost---because the costs are shared by society.
The short term demand for parking is relatively inelastic---so right after introducing pervasive charging for curbside parking and dropping minimum parking requirements for new developments, we will see roughly the same number of cars parked. (That's where your dependency comes in.)
In the longer term, demand for parking is more elastic. (One can see a similar relationship between oil price and demand for gas guzzling cars: inelastic / path dependent in the short run. More elastic with enough time.)
This holds even without public transport at all. Public transport is just one of the things that can serve as an (imperfect) substitute for private car rides. There are other ones, like car sharing, choosing job/home combinations that are closer to each other, telecommuting, home delivery of groceries, buying groceries in bulk, etc.
(To take one example right now, people already prefer to work closer to home, and make trade-offs all the time when considering a home or a job. The point of indifference between eg home price/salary and commute length will shift. Full disclosure: I hate commuting myself and have decided to fork out the money to live very close to the office.)
All the people in the market are probably much cleverer than me in coming up with substitutes. The price mechanism can guide them.
Some of these substitutes can and are provided by the private market. Public transport is generally not. Though eg Britain has privatised train companies.
Add in as another complication that without careful regulation, lots of public transport options are natural monopolies. One attempt to blunt this effect is by careful separation: eg run the rail network as a heavily regulated, public utility and make private companies bid for the right to run trains on it and for slots at the stations etc. And be very careful to specify that apart from meeting some minimum standards, the height of the bid alone determines the winner of the auction---politicians like beauty contests, because it gives them power to meddle.
See https://en.wikipedia.org/wiki/Privatisation_of_British_Rail for some lessons. Germany faces similar problems in eg their electrical power market.
Since I'm already on a tangent: the American freight train market and its history are another interesting piece to learn from. (It's doing pretty well, mostly because they don't have many passenger trains clogging up the network like in Europe, and the new regulatory environment of the Staggers Rail Act (https://en.wikipedia.org/wiki/Staggers_Rail_Act) seems to have worked out reasonably well. (They called it `deregulation', but that almost never happens---it's just a different form of regulation.)
[#] Zero in terms of dollars plus the effort and hassle of congestion and cruising for parking.