The problem with aerosol injection is that it doesn't actually lower CO2 levels. It just adds a cooling effect that can counter the CO2 warming effect. The aerosols don't stay in the stratosphere long so you need to be regularly injecting more.
If you stop those regular injections the warming quickly comes back.
If we have a strong plan to reach near net zero CO2 emissions in some given timeframe and we really can stick to it then adding aerosol injections so that we can stop the warming sooner might be OK.
If we don't have that there is a good chance that some large emitters will decide that since the aerosol injections are holding warming at bay there is no reason to not increase emissions as much as they want. Most will acknowledge that we should reduce emissions, but with no immediate consequences they will put it off.
Then in a few decades if something disrupts the regular aerosol injects we could get decades worth of warming over a few months.
That would not be good.
Human CO2 emissions will eventually decline naturally due to the meteoric rise of solar and the eventual exhaustion of economical sources of fossil fuels. We can't increase fossil fuel consumption forever, and CO2 will not continue to rise forever. But it will rise to a point where we will need to implement a proactive solution for warming, regardless of what the EU does or doesn't do. Pretending that emissions reductions alone are going to save the world is doing everyone a disservice.
What makes you think we‘ll do better at more complex solutions?
A solution that can be unilaterally implemented by a small minority is much, much easier. Solving technical problems is much easier than changing human nature, which is in fact impossible.
What you call technical problems could mean global disaster if we make a mistake or overlook a side effect.