The nice thing about space mirrors is that of all the climate mitigation methods I've heard, they are by
far the most controllable. Solutions like "let's stuff the oceans full of iron to grow plankton to absorb CO2", even assuming they work as intended, have the problem that they are irreversible. Space mirrors can put heat where we want it, and remove it from where we want it, and can do so on hours of notice. It's actually the
least simplistic solution. It also actually allows some reasonable engineering experimentation with commensurate levels of commitment.
Unfortunately, it is also the easiest to turn into one hell of a weapon.
Then, following that logic, climate control in general is one hell of a weapon. If anybody actually can control the climate, can we allow them that power? Things like "turn it over to the UN" aren't a magical answer to that problem because "the UN" is ultimately just another group of people, not particularly imbued with magical resistance to the temptations of power. (Arguably, quite the opposite.)
But assuming the massive political problems can be solved, problems which all climate control schemes have equally, space mirrors are actually the one I favor most. Too many of the other ones have a failure case of "triggering an ice age", and for all the words spent on explaining how bad global warming is, ice ages are several orders of magnitude worse than the worst global warming story I've heard. A true ice age is the end of civilization.