Stem cell research is, like many other kinds of biological research, essential to understanding how living things "work." It has high potential for advancing therapeutics, and thus falls into the "not just good but important to do" category.
Basic research should be funded by the government as well as private entities, because private entities often choose to use research results for private profit, not the welfare of the whole. Research is scientific infrastructure, the way that roads and bridges and water treatment plants are physical infrastructure. We need to support that infrastructure. In a straitened research budget, stem cell research might not have priority over something else--but if there were funds enough, it certainly should be publicly funded.