One of the ways people try to frame the challenge of climate change mitigation is "natural" solutions vs. "technological" solutions. We all have this intuitive sense that nature operates in a kind of balance - and if we have inadvertently or knowingly upset that balance; maybe it will be like a porch swing - continue to sway for a while but gradually return to equilibrium.
And that is true in some sense. There is a vast amount of carbon in circulation on this planet - far more than the fossil-fuel-derived bit humanity has added. It has been in a somewhat steady equilibrium that drifts around over periods of tens- to hundreds-of-thousands of years. If we "walk away" then equilibrium will return over the next millenium or two. But the great species diversity we have now will be gone; some new species will no doubt arise if we REALLY walk away. The biosphere will adapt.
But if we want to retain what we have, the natural systems need help. Whether it is growing giant kelp in the tropics, grinding mountains to dust to accelerate rock weathering, erect great machines to clean the air, transforming our agriculture to sustainability, restoring and expanding the worlds forests, or most likely ALL of these and more - they will be human technologies; applications of science and engineering to transform the local environment and our own capabilities. So there is really no nature vs. technology issue - everything we do to restore the climate is rebalancing nature, and all of it will require us to use technology.
Frankly speaking, I think that at this point we've disturbed natural systems to the point that we're kinda responsible for maintaining them anyway. Like, the following isn't a CDR example, but the hydrology of south Florida used to work a certain way, but then people took over managing when water flows where, with such things as the building of canals and artificial straightening of rivers, originally out of the hubris of thinking we could do whatever we wanted and later out of necessity to keep things from becoming a horrible mess...we kinda have the responsibility to maintain things now. In a way, one could remark that we thought we were God, and we took over such a role, and now we're stuck with the responsibility, and we can't exactly turn back the clock. So we'd better figure it out, one way or another.
I think like CDR, the hydrology of south Florida would eventually return to "natural" but like the carbon cycle, if we wait for nature to do the restoration, we are not going to like some things about that path - it will inconvenience us, you might say. In the case of hydrology, the responsibility is to ourselves mainly, whereas for the carbon cycle, a lot of other species are along for the ride.