Deserts are an important ecosystem and do have their share in cooling the planet, cf. https://climatefeedback.org/claimreview/deserts-cool-the-pla...
Here's the view from NASA's JPL [1]. They say the idea has merit. It's obviously not a silver bullet, and any planet-scale project can have lots of unintended consequences, so one needs to proceed cautiously. But one should not dismiss outright any solution because one identifies a negative side-effect.
[1] https://climate.nasa.gov/news/2927/examining-the-viability-o...