The ocean is the easiest effect to prove, but then there will be other unknowns of altering the air to have more CO2 and a dimmed sun.
You’re awfully cavlier about the one inhabitable planet we have.
I agree that there are big unknowns but I don't think that detracts anything from the point I'm making.
But that still leaves us with the other symptoms (ocean acidification) and unknown side effects.
So it's not a cost benefit analysis, because it only looks at the known costs. Here the known downside of an acid ocean and the unknown cost of side effects dwarf the actually calculable financial costs.
If we could run a thousand earth simulations we could speak of cost benefit analysis. But we just have one, and we know the conditions we grew our civilization in.
We may well have to do sun shading regardless, but we shouldn't call it a mere ten billion.
Edit: I guess to more properly respond to your original point: things may get very bad even if we do sunshades. Just via other mechanisms. Having the option will likely encourage a much higher co2 level than without sunshades.
I don't think we will ever see 5 degrees of warming if sun-reflecting particles work, and chances are they do.
[1] https://www.nature.com/articles/d41586-018-07533-4