Asset values do rise with inflation, and that itself doesn't make the owners of capital any better or worse off. But in an extremely low inflation environment,

Asset values do rise with inflation, and that itself doesn't make the owners of capital any better or worse off. But in an extremely low inflation environment, owners of capital can collect rents on their capital which will generate a consistent return that won't be destroyed or devalued by inflation. The relationship between inflation and inequality is pretty complicated because there are a bunch of other factors (notably growth) that play a significant role. I just wanted to point out that the economics of inequality does not support OP's argument (i.e., inflation creates inequality).