This analogy simply doesn't work because transit isn't fungible. Trains and air travel or cars simply aren't "the same park". The benefit of trains is objectively not just the carbon footprint. The money spent by the government benefits the public in other ways, not just environmentally. Ignoring the wear on (and cost of ownership of) personal vehicles, for instance, dismisses a huge amount of savings for folks who can take trains instead. Rail travel is safer and results in fewer deaths. The list goes on. Even "having a train that takes me to work so I can relax on my commute" is an important one. And many of those things are almost impossible to truly quantify the monetary value of and jam into a spreadsheet.
All the things you listed are examples of "other axes" that I listed as being valid objections. I also agree that it's hard to estimate the dollar cost or benefit of these things. But I think we do have to attempt to estimate it, since we have no other sensible way to decide how to allocate public funds.
It's not even all that difficult to estimate, really. For example, every business does it, of necessity.
Markets are a useful tool that societies use to optimize certain kinds of capital allocation and goods production, where that makes sense. No more no less.
Most of the things societies value most highly don't fit into the market hole.
If trains were exclusively a mechanism for capturing or avoiding carbon, then the metric of $ / tons would be valid. Trains very obviously are not that.
> It's not even all that difficult to estimate, really. For example, every business does it, of necessity.
This isn't even true. I run a business, and I frequently make decisions based on what I believe to be the right thing to do rather than what the data shows as being the most profitable outcome. The very notion of a "loss leader" is driven on fuzzy data where execs simply hope the loss in revenue from sales is made up for in other benefits that can't be concretely valued.
Numbers vary around the world, but FEMA in the US decided on $7.5M in 2020.
Financial investments are economic decisions. Whether or not you like the idea of assigning financial value to fuzzy concepts like happiness or quality adjusted life years, you still have to do it. The simple act of choosing to spend $N or not choosing to spend $N puts an implicit price on the result.
By putting approximate numbers in the spreadsheet - no matter how crude - we can at least end up consistent and fair. Otherwise we could end up spending vast sums to make a few people a little happier instead of smaller sums to make lots of people a lot happier.
No, but we can look at the amount of misery, that is prevented by not using cars. Traffic jams, pollution, accidents, waste of resources,...
The difference is so huge, we don't need to put a number on it. Public transport might be unpleasant for the individual, but is clearly very much better for everyone than using cars.