I think this is a decent and brief response to why geoengineering is a bad idea: https://www.geoengineeringmonitor.org/reasons-to-oppose/

The most convincing argument to me is that we're already facing a vast problem that would require a great deal of geoengineering to counter. If polluters realized they could geoengineer the problem away, they would stop trying to reduce emissions, and the geoengineering problem would become even larger and more unmanageable.

Due to how entropy works, it's always more efficient to simply not spill milk on the floor than to mop it up. Deciding that you should just have a milk bottle fight because you have a mop in the house is... strange? It will never be more efficient to scrub greenhouse gases from the air than to avoid emitting them in the first place.