Re: So... how DO we get more of public good things?
To show that economics is a generally applicable set of rules, whether that qualifies it as a science or not, let's walk through the basics of climate economics.
Humans are subject to hyperbolic discounting. That is, we value the future less than we rationally should do. Our estimations of the costs (and benefits) of future events seem to go a bit wonky 20-30 years out and further. I link this with our being a species that by long experience (the time is longer now) has generally had about that much adult lifespan to enjoy. We might also link it with Sir Pterry's "grandfather".
Stern and his Review said that they way to counteract this was to use not market interest rates to estimate the future, but much lower rates not subject to that hyperbolic discounting. He's right in theory.
Sir Partha Dasgupta said the theory is right. But the actual rate is far too low. Because, if we accept Stern's rate, then rationally we should be investing up to 98% of current income in investing for the future. On very much the grounds you are thinking about science on. Because we should value the future being richer than we are more than we do, and if we do that at the rate Stern says then that's the amount of our current income which we should be spending on that knowledge that will make the future richer well after we're all in our (paupers') graves.
So, the framework within which economics thinks about this, and climate change is a public good (although when it's not good we call it a negative externality) just as future MOAR SCIENCE is a public good, is what is the discount rate we should be applying to the costs of foregoing current consumption to gain that greater wealth for the future.
98% of current consumption for MOAR SCIENCE won't get past most peoples' bullshit radars even if people seem to accept it for climate science.
Ultimately though it comes down to what you think economics is, normative or positive. Should we be describing what ought to be done or should we be describing what is done? And if we take the positive route (which most economists generally try to do) then we come back to, well, people seem to value future MOAR SCIENCE at rather the interest rates that they view most other things in the future. At market interest rates.
Perhaps, according to some standards, they shouldn't. Maybe that hyperbolic discounting is "wrong" in some manner. But that is how humans act and it is us humans we're trying to maximise the utility of.
Alternatives have been tried: the Soviets spent vastly more as a proportion of current production on science than we ever have done. Pretty spiffy stuff came out of it too. But it was few peoples' definition of the desirable society.
Leading to a weak conclusion: spending on future public goods should be what people will put up with having taken out of their current consumption.