1. To state there is no technical solution is assuming you have all of the knowledge there ever will be in the world to make that assessment. A more proper way to state that is that you don’t know a technical solution, and there may or may not be one. There’s no reason not to do everything we can and research all options.

2. Having the ability to control the amount of sunlight hitting the Earth would help prevent overwarming, which is one possible outcome, and neither thermonuclear war nor any culling of humanity would be a solution, as in fact we’re responsible for this, so we must fix it. You’re basically suggesting killing all the life that could help.