Since LHC isn't a vanity project your whole argument breaks down. Also, climate change is largely not a topic for science, but for politics. Politicians know what to do, they just don't want to. No amount of science can fix this.
P.S. spending money on something that adds no clear value is the definition of a vanity project.
P.P.S. My argument also doesn’t hinge on whether the LHC or its successor is a vanity project or not, I think we can all agree spending 20bn+ on lifting people out of poverty or combatting climate change is a much more worthy recipient of tax payer dollars.