Depends on your political values. Many people think it is mandatory for governments to directly tax products with large negative externalities enough to price in those externalities. If a fossil fuel extraction system poisons a river, that needs to be priced in. If the government fails to tax what is mandatorily society's due, then it is a subsidy. Because we have to pay for the poisoned river in other ways.

> fossil fuels are under-subsidized by trillions of dollars because they are used to power hospitals

Nope. Governments/patients pay hospitals for their services, then hospitals pay power companies the market price for their services.