You can't undo all the damage. For example coral reefs are gone for a long time once they're dead. It's also unclear whether we haven't set off, or will set off, any feedback mechanisms that make it much harder to revert the climate to preindustrial times, for example because millenia old permafrost released massive amounts of Methane.

OK, let's assume you can't undo what's already done. However, if there is a choice between "let's consume less, shut down production, adapt to a less comfortable lifestyle and be extra careful about the environment, so we won't damage it again" and "let's engineer a process that negates the damage we are already doing, keeping our nice comfortable lifestyle", isn't the second choice more natural and rational?

I'm of course in favor of any solution that allows us to do less damage, but I think it's unlikely that we'll figure something out that allows us to continue burning fossil fuels at the rate we're currently doing. Doing both, reducing our reliance on fossil fuels, and figuring out methods for undoing what damage we can seems to me to be the best strategy.

Fossil fuels will last quite a long time. CO2, however, seems to be a greater problem.

Nuclear energy has nearly zero carbon footprint, though. With the closed nuclear cycle (breeders) uranium will last for millions of years.

Now you only need to convince everybody that nuclear power isn't literally the devil. And I guess you'll need some taxes to pay for the CO2 scrubbers.

egregiously false dichotomy

No, it means that you shouldn't bet everything on the hypothetical ability to undo any damage and maybe change your behavior so that you do less damage in the first place.

Oh, you broke an egg. Well, the next guy can probably put it back together. It should be as easy as breaking it, right?

It makes no sense to first burn coal and then try to suck out the 400 PPM CO2 from ambient air. And where are you even going to store it?

Today we can do nothing without breaking eggs. Non egg-braking technology is on the pipeline, and getting perfect. We will almost certainly switch to it soon. Egg restoring technology is further away, but it does not have to be easier, because we will have mostly stopped breaking eggs when we get there.

The egg is already broken. We can stop breaking more eggs by either tying our hands, or e.g. strengthening the eggshells or engineering some other compensatory solutions. We are humans, who are engineers. We don't like our hands tied.

The sense is energy extraction.