The sulfate concentrations required to meaningfully reduce solar radiation is orders of magnitude below the level that causes acid rain. The Tambora eruption didn’t result in global acid rain (though it did in Indonesia, naturally) while cooling the globe by at least half a degree Celsius if not more. And on top of that, there are other possible aerosols we could use, like calcium carbonate
I’m not sure your example supports your claim. We got an half degree cooling and all it took was the biggest eruption in recorded human history. Plus everyone’s crops died and the sulfur compounds caused lung disease.
That would require global consensus and could ignite wars if there isn't global consensus. Seems very likely that this could have unanticipated consequences that could be worse, but admittedly this is an area I don't really know much about.