Some pollutants do have a cooling effect and there are circumstances where purposefully increasing those pollutants could be worth it, but only if we can be sure it is temporary.
The nightmare scenario would be something like we start releasing sulfates into the upper atmosphere to induce cooling to counter the warming from greenhouse gases but do not reduce the growth in greenhouse gases.
Greenhouse gases would continue growing and so the amount of sulfates we have to release to counter that also would keep growing.
There are two big problems with that.
#1. The greenhouse gas emissions are a side effect of numerous useful and important activities. People make a lot of money from those activities. They happen unless we make a concerted effort to reduce them.
The sulfite emissions on the other hand would be specifically to counter the effects of greenhouse gases. Whoever is paying for them would be losing money doing this. All it takes is an economic downturn to make budgets tight and funding might go away.
#2. Greenhouse gases can affect climate for a long time. It takes hundreds to thousands of years in the case of CO2 for today's emissions to be no longer affecting the climate.
Sulfates in the upper atmosphere clear out in months to maybe a couple years.
Let's say then we go down the sulfates path, don't reduce greenhouse gas growth and this goes on for decades. Then something stops or disrupts the sulfate releases for a couple years and the sulfites leave the upper atmosphere.
The greenhouse gases are there still there and we rapidly get most of the warming that had been held off for decades by the sulfates.
This would likely be disastrous. Getting all that warming spread over several decades at least gives people time to adapt. Getting it all over a few years would be way to fast for people to deal with.
I think probably the only way purposefully emitting pollutants like this might be acceptable would be after we've got greenhouse gas emissions under control and are on a path we are sure is going to get is to net zero in some specific timeframe, but it will still take a few years to reach peak greenhouse emissions and we've identified a tipping point that we will hit before that. Then maybe countering that with emitting pollutants just until greenhouse gases peak and then come down to where we are below that tipping point might be reasonable.