Earlier quoted context omitted.
Since there is more space, you'd expect that the market would allocate more of it for parking where needs be and that you don't need the government dictating parking minimums. Also, not all space is equal: even in the US, well-connected space with lots of amenities like the downtowns of cities is not infinite.
The market allocates only as much as users can bear, which is about epsilon above the line of "for average user, the parking situation is so bad and unbearable that they chose to go without the service". Anything above it is money left on the table.
The total cost of a housing unit with parking wouldn't be be more than it is now because the cost of constructing a housing unit with parking wouldn't be more than it is now. It would just cause units without parking to become available.
Which would tend to increase housing availability, which would tend to lower prices including for units with parking. Because the people who want the parking spaces wouldn't have to bid against people who just want housing and don't need parking.