But one notes that the Romans managed to produce fair quality steel without coal. Certainly coal allows for industrial quantities of steel.
So all we require is an energy source that can provide enough heat.
Many societies did produce good quality* steel, but it's very expensive and only available in very limited quantities. Limited quantities means it just isn't available to be used for anything other than very specific, niche uses. And that really is the problem - so many other technologies rely on a number of other technologies to come to fruition (Sid Meier's Civilization) that removing or really hindering a single but very important technology stops the tech tree from continuing.
The thing about affordable iron and steel is that all of a sudden you've got a material that can be used in numerous applications - that availability and affordability drives innovation and hence technology.
*quality is relative - steel produced 100 years ago using cutting edge tech is considered very poor and dirty (impurities/inclusions/slag) even by standards 40 years ago let alone today.
Coal is not only cheaper and more energy dense than charcoal, but also allows for far greater temperatures in the" stack" which improves reaction rates and overall efficiency (converts more iron oxide to iron for a given weight of ore). Higher temperatures also mean that more impurities are removed due to slag fluidity and higher reaction rates. Coke (sintered coal) is also far stronger physically than charcoal so you can stack a greater amount of charge (iron ore/limestone/coke) which again improves efficiency.
It also provides the carbon for reduction of the iron oxide.
Now of course we could use a carbon substitute to reduce the ore but getting that heat is the problem. Approximately 45% of all electricity generation in the UK is based on burning coal as I type. There really isn't any other fuel that I can think of that can produce the heat required in such quantity so easily without advanced technology to a) mine/extract it b) use it.
Don't forget that extraction and processing is only half the story. You also need power to manipulate (forging, cutting, stamping, grinding etc) the material you are producing. It's fine to cast iron into shapes ready for use in a design, but how do you join the stuff? Rivets still require heat to increase their malleability and ductility. We'll leave arc welding for the time being!
It all comes down to that all important heat.
It is probable that electricity and the nuclear model of the atom could be discovered even without the coal driven industrial revolution we saw. It would take longer, granted.
Electricity took something like 300 hundred years (from roughly 1600 to 1900) to go from a scientific novelty to a daily reality and start to impact people's lives. Even then you could add another 50 years tio that figure for the impact to be universal in the western world. I don't really see how the lack of coal could be too much of a hindrance to discovery. Lead, copper and acids (battery) can all be produced without coal and scale isn't a problem so I agree that scientific discovery isn't a problem.
However, once again we come up against the difference between discovery and use; science and engineering. It's fine to discover something, but it requires a whole load of other factors to be present for a new discovery to produce any benefit and hence; the modern world.
Lets say you have enough iron/steel/brass/copper/bronze to produce a steam engine (running no fossil fuel) and motor which in turn produces electricity. Now imagine if there was absolutely no way to transmit that power because there was no way of producing enough copper to make the cables because there's no fossil fuels to smelt the copper in the first place. So what do you do? Well you use your new steam engine to produce electricity to smelt the copper! What does your steam engine run on again?
The electric light bulb may well have been invented and demonstrated but there is just no way that anyone can afford the link between the generator and bulb.
However once discovered and developed, electrical production from wind and hydro could then drive an industrial revolution similar to ours. Soon after(say 200 years) would come nuclear power, and a second much stronger international revolution in trade as ships would no longer rely on sail.
Not a hope in hell. Nowhere near enough power. Not even today would that be possible.
You simply cannot extract enough energy from wind to get anywhere near enough power to start powering electric arc furnaces for steel making without first going through the industrial revolution and 20th century advances that provide the infrastructure for wind power to be distributed to such facilities in the first place.
How are you going to produce the steel towers, the steel bolts without first having a steel industry in place? What is powering that industry?
How are you going to build the concrete bases (yes I know the Romans had concrete) without a concrete industry? How do you even transport the concrete to the site when the internal combustion engine isn't mass produced and the vehicle to haul the concrete to site is made of iron/steel that cannot be produced in any quantity?
How are you going to manufacture the gearbox? The gearbox is going to transmit power from the blades but this requires advanced technology, mechanical engineering, manufacturing engineering, electrical engineering, materials engineering, control engineering. mass production, process control, quality control, etc, etc.
Then you've got the blades which aren't made from metals or alloys. Where does the advance in non-metallic materials come from? How is it possible to develop composite material technology with such a limited understanding of materials in general because the sciences of metallurgy and chemistry haven't advanced? How can you go from cotton and hemp cloth to glass and carbon fibre reinforced composites without some form of academic/technological/engineering structure and the society that provides it?
Hydro-elecric power in Canada is one of the reasons why Aluminium and it's many alloys is so prevalent today. Cheap electricity close to the source of ore is a massive bonus. However, you need sufficient technological advancement to be able to take advantage of a natural resource.
How would it be possible to produce the dams without enough mass transport or concrete (which is an energy intensive product to make) anyway? How do you produce all of the machinery in the turbine halls to produce the power and then distribute it when you are limited by your fuel source for producing precision engineered components?
How do you use hydro when there aren't any sufficiently good sites?
A world limited to wind and water power without a resource that provides cheap energy would stagnate. There is just no way that such a world can make the leap to advanced technology using wind and water power alone. It's energy starved.
I'd love it all to be milk and honey, but the truth is, without fossil fuels we'd never be typing our posts.