You can't sign up - at least not for long. As public transit improves companies quit putting in parking places up front - they still have shipping/receiving in back, but only delivery vehicles allowed. The parking lot is sold to someone else who just wants a building, increasing density. Meanwhile all those people riding transit means there is more demand for better transit.
The above plays out over decades of course, and there are lots of competing factors.
I think you’re misattrubuting causation here. There are numerous factors that distinguish those two places. Chiefly, they are among the densest places in the world.
Generally speaking, cars are at odds with such extreme density, simply due to geometry (i.e. how much space driving requires); it’s super easy to saturate driving supply in such places.
Think of mass transit and driving as being in an equilibrium with each other. Depending on where the bottleneck is in driving supply, shifting driving demand to transit demand (via improved transit infrastructure) should most often improve driving.
Extreme density like the places you mentioned is challenging just because space is at such an extreme premium. I would argue (and I’m not alone here) that it’s especially challenging because driving is consistently underpriced; the fair value of driving there is likely far higher than the cost that drivers pay. In such circumstances, oversubscribed car infrastructure is the natural outcome.
The above plays out over decades of course, and there are lots of competing factors.