A scheme to cool the whole planet can only be tried at the scale of the whole planet, so there is no small trial run that shows its side effects first. Calling such tinkering 'cheap' ignores that its costs are unknown, not low.
Offering a technical way to undo a problem reduces the pressure to stop causing it. A promise to reflect sunlight away can become a reason not to cut emissions. This is the moral hazard of a quick fix.
Any tool that can push the sky around tends to be taken up by militaries and could be used by one country alone against everyone else. History suggests climate engineering would follow the same path, while no body has the wisdom or authority to govern it.
For more than a century, people promising to make rain or tame storms have claimed far more than they delivered. Some were frauds who sold farmers rain or gave clients the forecasts they wanted to hear. Today's climate engineers repeat the same overconfidence.
Speaking of 'fighting' or 'battling' climate change frames the sky as an enemy, so the natural response becomes to attack it with rockets and lasers. Once the problem is treated as a purely technical contest, its political, ethical, and social sides drop out of the discussion.