Then just tax that. Effectively giving public transport the ability to collect taxes in small pockets of your land around public transport stations seems like an odd way to go about it.

You could similarly run the police at a profit instead of being a cost center by gifting 100 hectares around every police station to the police, and have them collect rent on it. That doesn't make sense either.

For one, it creates a perverse incentive where the government can't let property prices fall for the common good least their public transport (or police) services would go out of business.

Hong Kong famously has a problem with this. It's a relatively low-tax regime with absurdly high housing prices, because they raise a much larger part of their revenue by taxing land than most other similarly developed areas.