The reason why "kilogram" is the name of a base unit of the SI is an artefact of history.
Louis XVI charged a group of savants to develop a new system of measurement. Their work laid the foundation for the "decimal metric system", which has evolved into the modern SI. The original idea of the king's commission (which included such notables as Lavoisier) was to create a unit of mass that would be known as the "grave". By definition it would be the mass of a litre of water at the ice point (i.e. essentially 1 kg). The definition was to be embodied in an artefact mass standard.
After the Revolution, the new Republican government took over the idea of the metric system but made some significant changes. For example, since many mass measurements of the time concerned masses much smaller than the kilogram, they decided that the unit of mass should be the "gramme". However, since a one-gramme standard would have been difficult to use as well as to establish, they also decided that the new definition should be embodied in a one-kilogramme artefact. This artefact became known as the "kilogram of the archives". By 1875 the unit of mass had been redefined as the "kilogram", embodied by a new artefact whose mass was essentially the same as the kilogram of the archives.
The decision of the Republican government may have been politically motivated; after all, these were the same people who condemned Lavoisier to the guillotine. In any case, we are now stuck with the infelicity of a base unit whose name has a "prefix".