Why is the goal to get something "stable" in the first place?
Climate on earth never was and never will be stable, so this should not be our goal in the first place.
The goal should be to keep the change fairly slow because most living things have trouble with fast changes. That's it we don't need more than that.
"Fairly slow" on an evolutionary timescale and "stable" across human timescales are functionally the exact same thing.
The difference between the two is negligible compared to the difference between either of them and what we currently have, which is "unprecedented" on human timescales and euphemistically "radical" on evolutionary ones.
You might as well say "look I just don't understand why people say we need to stop the car, obviously slowing down to walking speed would be enough" while the car continues to accelerate at full throttle towards a cliff edge.
But no one knows what "fairly slow" is.
Also the climate collapse theories predict that once a certain tipping point is reached, its game over. If that is true then slow and stable increase still gets us to that point just a bit later.
In other words to make climate change stable do we need to reduce CO2 emissions, completely stop CO2 emission or remove CO2 and reduce the CO2 in the atmosphere?
We don't even know which of these 3 options would lead to the "fairly slow/stable" we want.
It seems like we just do all 3 with no evidence of any real world effect whatsoever.