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.
Another important distinction to make for those that might not be aware: in the US, mortgages mostly are a set-rate when the loan is issued, usually either at 15-years or 30-years. In most of the rest of the world, I'm told, mortgages are typically variable rate
This is a bit like saying earnings going up isn't good for stockholders, because they would have been charged a higher price to buy the stock if people had known the earnings were going to go up.
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.