These are good examples and it’s even worth noting that the net impact of these can be a huge boost to the market. But it is a local and greedy optimizer. It doesn’t think “would having public transit improve the economy long term” it thinks “could I make enough on fares to justify the investment” (which is almost always no, at least relative to other investments). This is the nature of positive externalities. They are value that the market is unable to weigh in its decision making.

Yes, as you say the market is a local (both in space and time) and greedy optimizer.

Long-term payoffs that increase the value of all participants in society, such as education, healthcare, infrastructure (roads including public transportation, water, electricity, ...), are demonstrably better served by government than by business.