It is already rewarded for those benefits, that's what the money is for.

So there are no positive externalities to good health, transportation, manufacturing, climate control, or the millions of other uses for fossil fuels?

Those are benefits that are explicitly paid for, that's why we are using them. We don't buy them for other reasons then just get climate control by accident.

An externality is a cost or a benefit that is not accounted for in the trade.

The massive number of COPD cases are not paid for when fossil fuels are burned. The good things we get from fossil fuels is why we pay for them, that's their value and it is accounted for.

Aren’t there unaccounted for benefits to 3rd parties from me being able to get to work or the grocery store, heat my house, or the million other things I use fossil fuels for? Just as there unaccounted for costs?

Edit: I guess what I'm saying is that I really have no clue what you're suggesting here as a potential external benefit. The external costs are well documented, but I don't understand what you are trying to say is the unaccounted for benefit.

If you think that those things are more valuable than what fossil fuels charge you right now, shouldn't you call up your utility and offer to pay more?

What sense of "value" are you using here? I like to live, so I find food to be a great thing, so perhaps in one sense the value of food is infinite, but in a much more useful sens of value I pay something that it much closer to the cost to provide it than how much I would theoretically pay if my choice were to go without.

In the case of food, what happens when the manufacturer uses a new additive in their food that happens to decrease your lifespan by 1 day every time you eat one serving. It just happens that this additive is cheaper than the previous ingredient that was used for the same purpose (as happens so often color / texture / ...) The manufacturer receives a benefit (decreased cost) while pushing the cost (decreased lifespan) on you, the consumer.

Now recognize that this happens across all industries in the world every single day. New things are discovered that displace old things. We don't know all of the consequences for the new shiny product when we start producing and selling it to mass markets. Sometimes the new things have major disadvantages that we just don't know at the time we start using them. Look at historical problems with CFCs (which lead to ozone holes in the atmosphere) PCBs (which cause birth defects and can cause cancer), or how neonicotinoids impact insects (which can lead to the deaths of beehives). If the vendor pushing these products had to bear the full cost of the consequences of their use, they might never have been widely accepted. Capitalism is and always will be imperfect in this regard.

Though externalities are a well-studied phenomenon and failure mode of capitalism, I think that it will be a problem for nearly any conceivable economic system. Any economic system will have to deal both with unintended and unknown consequences, as well as with any harm/benefit to society that is not accounted for in a trade.

presumably the benefits are priced in.