While it's true that, a priori, there's no reason that ethnic homogeneity should be a prerequisite for a welfare state, this idea is misleading because it supposes that all ethnic groups contribute to the welfare state equally. I know that it's modern dogma that all groups are equal in all respects, but hear me out: what if they're not?

What if, for whatever reason, ethnic group A subsidizes B's existence? This difference will damage the social cohesion necessary for a welfare state to exist. In the real world, we observe huge group differences in productivity, educational attainment, conscientiousness, fecundity, and other characteristics, and in the real world, we see that mixing groups does indeed damage social cohesion. I understand that this observation is unpopular --- but this unpopularity doesn't make it wrong.

I don't think it's politically possible to create a strong welfare state in a country populated by identifiable groups with differing socioeconomic contributions to the common good.

Others have commented that it's the size of the country that makes welfare impossible --- that it just doesn't work over a certain size. As a practical theory, I think that's true, but I don't think size itself is the root cause. I think that as a country's population increases, the visibility of low-contributing groups increases, and it's this visibility that reduces the will to create a global welfare state.