The page you link to explains:
When defining fossil fuel subsidies, it is important to distinguish between consumer and producer subsidies. [...]
Subsidies are intended to protect consumers by keeping prices low. [...] All consumers—both rich and poor—benefit from subsidies by paying lower prices. Governments could get more “bang for their buck” by removing or reducing subsidies and targeting the money directly to programs that help only the poor.
I guess here it gets the political point that giving money more directly to the poor is seen as a bad idea. Although the IMF doesn't get to explaining this beyond:
The absence of public support for subsidy reform is in part due to a lack of confidence in the ability of governments to shift the resulting budgetary savings to programs that would compensate the poor and middle class for the higher energy prices they face.
Banque de France for example does go into that kind of explanation
that for a different subsidy, one that subsidizes the minimum wage, but it's essentially the same idea that giving money to companies is better than giving it to the poor directly:
Among mainstream economists, minimum wage
is viewed as the archetypal bad redistributive
instrument. Basic income or negative income tax are viewed
as far better instruments. [...]
The opinion against minimum wage fails to recognize the separability property between
an allocative purpose efficiently done by the markets
a distribution purpose reached through a
redistribution of property rights
Basically, it is the 2nd fundamental theorem of
Big if: optimal lump sum transfers can be
Lump sum transfers are difficult to manage
Optimal lump sum transfers cannot be implemented (Mirrlees “the curse of talented people”) [...]
Suppose that we couple the minimum wage with a firm
subsidy (a solution experimented at a large scale in France),
the two solutions are not that far.
We can always increase the firm subsidy up to the point
where the labour cost is no more than the equilibrium
If so, then the two solutions appear quite symmetric
– The firms pay no more than the equilibrium wage
– The workers have both the same disposable income
– The only difference is that we subsidy firms instead of
We prove [...] in the following that maybe contrary to the
intuition, the minimum wage coupled with firm subsidy is a
better second best instrument. The reason: the benefit of the firm subsidy will be entirely
pass through firms because of the minimum wage – While some part of the worker subsidy will be passed through firms.
To get some equivalence like that for consumer prices requires coupling subsidies with maximum/cap prices (I think), i.e. some kind of price controls. That IMF page doesn't actually mention the latter though, but I think they are fairly widespread as well. The World Bank mentions however that
The low [end‐user prices] prices [for fossil fuels] arise because of price controls in many countries.
The International Institute for Sustainable Development also mentions that:
Price controls, market access limits and trade restrictions are also often a key element of fossil-fuel subsidies.
(I'll try to get some more numerical details on this later; somewhat surprisingly hard to find...)
For example, a United Nations Environment Programme (2016) says e.g. about Indonesia
The last series of reforms implemented by the Jokowi administration in 2014 attempted to finalize a complete reform to peg the domestic fuel prices to the global oil market and to remove price controls under the rhetoric of the need to reallocate the budget towards infrastructure investment, particularly in the energy sector. The government received advice from bilateral and multilateral development organisations, such as the World Bank, JICA, ADB, on how to best to redistribute the subsidy budget.
[...] However, the [price control] reforms were not implemented because the
rupiah depreciated to IDR 13,271 against the US dollar, levels not seen since the Asian financial crisis and fall of Suharto. [...] Consumer prices stayed the
same and the burden of subsidies was transferred to Pertamina, which covered the difference from the production costs and
market price of oil. The government did not reimburse Pertamina for losses from price controls during 2015, which amounted to
USD 1 billion (IDR 15 trillion). The 2016 budget will need to provide for Pertamina’s deficit to prevent it going bankrupt. Since
Pertamina is a state-owned enterprise, the government has a fiscal liability to recapitalize it. The fact that the price controls were
not fully removed means that the fossil fuel subsidy reform is incomplete.
So in this case the state-owned company was nearly bankrupted by the removal of subsidies that wasn't coupled with removal or price controls. (And of course, it was "bailed out" with tax payer money.)
And a couple of years later (2018) fossil fuel price controls were still in vogue in Indonesia (as were subsidies).
Indonesia still subsidizes some fuels and the government said in March it would cap domestic coal prices and keep fuel and electricity prices unchanged until the end of 2019, an election year.
Of some note, which may explain the IMF doesn't even mention price controls... it's because the IMF now includes price controls in consumer subsidies.
In practice, consumer subsidies are often implemented with price controls [...]
So, I guess if you want to ask from that broader perspective: why support the consumption of fossil fuels at all? The previous quote (about Indonesia) should give you some idea: [electoral] short-termism. Surely this can be phrased more gently as in James' answer "don't let gramma freeze while we build enough solar panels".
Futhermore, if you look in more detail at the IMF report, they charge the largest percentage to
"enviromnetal subsidies", meaning fossil fuels not being taxed enough in their view:
underpricing for local air pollution is still the largest source [of subsidies] (48 percent in 2015) [...]
For one thing, environmental costs are measured with considerable uncertainty—most obviously
global climate change, but another example is local air pollution, where there are several
sequential linkages between the burning of a fuel and changes in the mortality rates for exposed
populations [...], all of which involve plenty of data uncertainties. In addition, there are
differing views on how to value the associated health risks. Nonetheless, environmental costs are
just as real as supply costs, and undercharging for an unbiased (albeit uncertain) estimate of
them is tantamount to undercharging for the true social costs of consumption. Moreover, the
estimates presented here should be viewed as indicative
So, according to the IMF, not only should the obvious subsides be completely removed, but also fossil
fuels should be taxed more. Why aren't governments doing this? A simple answer: "yellow vests". Even in countries like the US which pay a third of what Europeans do as taxes on gas, there's a political commitmment (even from the Democrats) not to raise taxes on gas as it's seen as affecting the middle class. Furthermore, in countries that produce oil, it's seen a somewhat of a social entitlement to have cheap gas; from a 2017 news/study:
The good news for the environment is that two thirds of countries oversaw an increase in taxes or decrease in subsidies between 2003 and 2015. The bad news is that was outweighed by gas-guzzling in jurisdictions that eased the cost on motorists. Globally, the net tax decreased by 13.3%. [...]
Predictably enough, 22 “persistent subsidisers” identified in the paper are all oil producing countries. They include Ecuador, Angola and Gulf states, where citizens expect to share in the resource wealth.
“People in oil producing countries often view this as an entitlement,” said [lead author Michael] Ross. “Partly because they fear that they are not going to benefit in other ways from all of this oil money in places like Nigeria and Venezuela, they demand that they get their benefit up front in the form of cheaper petrol.”
Rewriting this social contract is a recognised challenge. Subsidy reform has sparked protest in at least 19 countries since 2006, the paper notes.
As for coal; consumer-side the story is basically the same.
Several countries also provide substantial subsidies to the consumption of coal-fired power. However,
there is very limited transparency, and these measures – and the resulting support – are not easily
captured. While we were unable to quantify a number of these measures, we know that Indonesia,
for example, provides over US$2.3 billion in fiscal support per year, with the stated reason being to
compensate electricity generators for the increase in coal prices and for having to sell electricity to
domestic consumers under regulated prices. Similar subsidies relating to provision of below-market
prices for electricity consumers also exist, for example, in China, Indonesia, Mexico, Russia and South
Africa, with much electricity for this consumption coming from coal-fired generation.
When it comes to coal production it's difficult to even say what's a subsidy (in the broad sense that the IMF calculates these, i.e. taxes being owed) since the coal producing companies in the two top producers (China and India) are state-owned by-and-large. So in that regard it's a bit like saying: the government should tax itself more. Although the fossil fuel companies owing taxes directly to the people isn't perhaps so outlandish, in theory, but not implemented anywhere like that, as far as I know.
Even in China, the idea of taxing the SOEs more is seemingly interesting though,
because despite the authoritarian regime, SOEs even there are apparently good at avoiding to pay dividends to their owner-government.
But of course there's the thing that in developing countries cheap coal power is (still) seen as the way to bootstrap themselves, so there's little government interest in taxing it more.