Will we avoid a crisis by migrating to other sources of bulk power before easy to reach oil runs out? Very doubtful.

It's a bit mixed up whether it's rebooting after a collapse or rewinding and removing fossil fuels from history, but either way I think it's easy enough to sketch out ways in which the world would be better without than with them.

Potential unexpected bad effects, Whales might have been wiped out for their oil?

But a reasonable amount of the industrial revolution was wind and water powered in real history.

Likely that we wouldn't have any trees left, either, were it not for coal. I'm going to get this a bit wrong, but my understanding is that what with making iron implements (whether swords or plowshares) and the like, England was on its way to being stripped of trees. Then coal was discovered. (There was a whole article months ago on HN, talking about iron production, and this particular point. Damned if I can find it, though.)

The deforestation of Britain happened in the bronze age, mostly for the purposes of agriculture.

The remaining woodlands were husbanded for centuries after, precisely for their use as a source of fuel and construction material.

At the very least, in the right hands that idea could probably make for an interesting short story.

Thermal-wise, the closest thing would be a huge solar farm to power or melt metals at a steel plant. It would just be more land-consuming.

As for earlier civilizations... the Romans didn't use any fossil fuels, but their large construction projects used mind-boggling amounts of charcoal for lime-burning, resulting in massive deforestation in the Balkans. And of course all early metallurgy depended on charcoal as well.

If the question is "Could we (re-)boot a modern civilisation without fossil fuels", then "charcoal is and was a widely-used, sustainable (and sometimes superior) alternative for things that fossil fuels were and are used for" isn't a "...but..." it's an "... of course ...".

So, to be clear, deforestation is a potential problem for any kind of wood usage. It is generically, an issue for all resources, fish, buffalo, bees, golden geese. If you need something, don't kill the source of it, is a good general rule to follow. Though if you're an invading army on foreign land, that generally doesn't impact on your long term planning as much as it should.

But, crucially for the question posed, wood can be managed as a sustainable resource, and is not a source of fossil carbon, so burning it, gasifying it etc., which almost certainly has "it's own problems" is not a problem from a carbon perspective, even though it releases carbon into the atmosphere when burnt.

Though another way to look at charcoal is to consider it as artificial coal.