But all things are not equal; lenders take expected inflation into account when evaluating the interest rate they'll demand on their loans. Only unexpected inflation is good for debt holders.
They also tend to be shorter than the standardized USA 30-year fixed.
Once you've taken out a fixed-rate mortgage, inflation absolutely has the effect of reducing the value of the debt you owe. It's more if you're about to take out a mortgage that you're rooting against (expectations of) inflation, as lower inflation will also serve to decrease the prevailing interest rate.