Why should a changed climate result in worse droughts in places that are susceptible to drought? Might it not lead to more rain in some drought-stricken places and less rain in some rainy places?
"Theoretical and climate model studies suggest that, in a climate that is warming due to increasing greenhouse gases, a greater increase is expected in extreme precipitation, as compared to the mean. Hence, anthropogenic influence may be easier to detect in extreme precipitation than in the mean. This is because extreme precipitation is controlled by the availability of water vapour, while mean precipitation is controlled by the ability of the atmosphere to radiate long-wave energy (released as latent heat by condensation) to space, and the latter is restricted by increasing greenhouse gases." --- http://www.ipcc.ch/pdf/technical-papers/ccw/chapter2.pdf
> Might it not lead to more rain in some drought-stricken places and less rain in some rainy places?
Yes, in fact some IPCC analysis suggests that North America will see e.g., increased crop variety and yields by 2080, and also e.g., a 40% decrease in Texan farmers' net income and more agricultural disease.
But although climate change isn't uniformly and strictly bad news, it is likely that some places will see catastrophic effects and that in aggregate the changes will be more problematic than beneficial for humans.