> Why not just get rid of mosquitos?
Because its harder than it sounds: LOTS of effort goes into eradication, whether by large-scale environmentally destructive methods (literally draining the wetlands where they reproduce), toxic methods (spraying poison over areas they reproduce near human populations, which also means over humans and water used by humans), or trickier methods lkke releasing masses of sterile male mosquitos to mate unproductively with females to reduce the number of productive matings.
But these efforts are usually less than complete successes at the best of times, and have gotten worse over time as—as the article here notes!—“Efforts to prevent the spread of the disease have been complicated by existing malaria interventions becoming less effective due to mosquitoes developing biological and behavioural resistance to insecticides and barrier-based controls.”
> It seems that elimination is actually easier.
It sounds like someone has never tried elimination.