No, it's better than installing artificial snow to reflect energy.
The snow doesn't change the energy budget of the earth at night, because there is nothing for it to reflect, and the infrared energy it emits is pretty much like the infrared energy from most other surfaces, and a certain percentage makes it off planet and the atmosphere absorbs a certain percentage.
The skypaint emits infrared in a particular bandwidth which the atmosphere does not absorb, called the "atmospheric window", so a much higher portion of it's energy makes it off the planet. This effect will operate regardless of whether the sun is shining on it or not, it will keep dumping something around 120 watts per square meter off the planet as long as it is exposed to the sky.
“Other than all the environmental damage, why not?” all the time. They weigh the likelihood of being caught or not, and do a cost/benefit analysis. They choose environmental damage just for a 1% increase in profit margins.
If they can do it, why can’t a properly funded radical geoengineering activist group do it?
Because they rule society and activist groups don't? Not sure what you're getting at. Obviously the rules in society aren't applicable to the ruling class, that doesn't change the fact that an activist group would be stopped by intelligence services before doing anything like this. Pointing out hypocrisy unfortunately has no power to stop it.
People are starting to study this. Basically it would be like installing artificial snow to redirect the light energy back to space.