Jimmy Carter told people the truth. (And he got promptly voted out, and so subsequent politicians have hidden the ball with the truth.) With respect to the environment, for example, he told people to put on a sweater. Because the truth is that almost all GHGs result from consumer-facing industries where
consumers are the primary beneficiaries of pollution being artificially cheap.
Concrete example, since you mention the oil industry: Exxon makes about 22.5 cents when you buy a gallon of gas at $3.00. Meanwhile, an analysis has found that gas should be taxed an extra $4.36-7.62 per gallon to fully reflect the environmental and other harms of driving: https://www.citylab.com/transportation/2015/01/the-real-reas.... So when the government doesn't impose that tax, who benefits? Exxon benefits a little because it sells more gas and collects the $0.22 of profit on each gallon. But the consumer saves $4.36-7.62 by avoiding those taxes. Exxon's profits, about $20 billion last year, are a rounding error compared to the trillion+ dollars that consumers would pay in extra taxes to address the negative externalities of driving.
Transportation, heating, agriculture, consumer products--these are the industries responsible for the fast majority of GHGs. And these are also highly competitive, commoditized industries where most cost savings get passed onto consumers. (Facebook makes more profit than Exxon, even though Exxon's revenues are more than five times as much.) That means the savings of making pollution cheap also accrues mostly to consumers. The industries where lack of competition allows corporations to command huge margins--banking, tech, advertising, etc.--are not the ones that are primarily responsible for GHGs.
"Access to healthcare" is similar. Why do people in Sweden have universal healthcare while people in America do not? Is it corporations? No, Sweden's corporate tax rate is quite a bit lower than ours. (It's similar to the current federal rate, but in the U.S. most corporations also pay a state rate. In Delaware, for example, it's an additional 8.7%.) So who benefits by Americans not having universal healthcare? It's middle-class Americans who don't pay the high middle-class taxes that middle-class Europeans pay.
Warren's focus on corporations is a total red herring, intended to make people falsely believe that you can have universal healthcare and a cleaner planet without decreasing your material quality of life. As Jimmy Carter told us, that's not in the cards. How do we know that? Because we can look at other countries who do better on these measures, and see what they do! France has much lower GHG emissions than the U.S. and universal healthcare. How do they do it? They live in houses that are half the size; they drive tiny fuel efficient cars, and have fewer of them per household; they deal with the challenges of nuclear power; their payroll taxes on the middle class are double ours; they take public transmit more often and therefore have significantly longer commutes. But their corporate taxes are even lower than ours!