Looking at the issue of inequality through the prism of one nation state is a bit absurd no? It'll be like saying inequality is solved because everbody in Andorra owns their own ski lodge.
And there really isn't any better way to reduce inequality between nations than by reducing the distorting effect of borders to nil.
I think this is a good point, because it isn't really just about inequality between nations, but also impacts inequality within nations.
If we live in a world where, thanks to the free movement of capital, technological advancement etc, the power of the nation state to implement redistributive policies has declined; then inequality between and within nations are really the same issue.
We would never be able to fully solve inequality on a nation by nation basis, as any redistributive policies around taxation or corporate and economic structures could always be undermined by a "competing" nation. The real answer has to lie in, at the very leaf, a global taxation structure and global regulations on corporate practice and ownership.
That said, nations still do have the ability to implement tax or regulatory structures, or even use mechanisms like subsidies, that could help reduce inequality. Such as tax breaks to co-operatives, or lending to help employees buy out their employers.