We should stop subsidies for all fossil fuels, and begin phasing in taxation of fossil fuels to account for their cost. But the cost I'm talking about it not just about money. There isn't a viable alternative to a whole host of products that we use. Off the top of my head I can think of plastics (huge) and large equipment. Even using energy-reclamation for garbage trucks is an "innovation" for us. We simply couldn't do it with the current paradigm.
You also have to consider that the majority of humanity is evolutionarily wired to be change-averse. Overturning our current infrastructure is not easy, and will require trillions of dollars of investment, for essentially the same level of service that we have today. That's hard to convince people to do. And even the best idea is worth nothing if people won't adopt it.
Most of the things I have read which accuse energy companies of being subsidized lack a basic understanding of the historical accounting mores of those industries. This is principally because of depletion allowances and industrial depreciation. Both of those still apply and have full standing in the law.
I am not saying this should not be changed but rather that it'd be quite a change.
As a USAian, I can expect my energy need to be met by cleaner tech than someone in, say Africa. Natural gas is here and will make a difference.
The major players in the fossil fuels industry are all net tax payers. If I'm understanding the summary from the linked paper, it's saying that they're not taxed enough for the satisfaction of the paper's authors. Thus they are being "subsidized".
