Now you’ve created a property tax regime where nobody is going to want to own residential property near a transit station.

typically people want to live nearby transit stations because it means you can get places cheaply.

the property value goes up because of increased demand for it

Do you mean that nobody wants property values go up? The government gets more property taxes, because properties near transit stations are more valuable than in other places.

Yes, if you don't intend to sell, and actually want to live somewhere, higher property values just mean higher taxes (or if constrained like with Prop 13, declining services).

This doesn't have to be true. Washington State, for example defines the amount of property tax revenue to be charged and then divides that in proportion to everyone's taxable value.

So if everyone's value goes up 40% your property tax bill stays the same. If your area climbed faster than others, it goes up but not by 40%.

If property prices increase 40%, then cost of living increases, government needs to collect additional revenue to pay employees a living wage, and that feeds into taxes. Even without higher order effects, the above chain was literally about net increases in property taxes to fund more services and saying it's fine because property values increase (in specific locations, too). But property values are not a tangible thing for anyone who doesn't want to sell.

declining services here would mean that transit station stops gwtting service though, decreasing your property value