The opportunity cost of cash is the return that you would have earned if you had invested in a risk-free asset instead of keeping the cash. By keeping cash you

The opportunity cost of cash is the return that you would have earned if you had invested in a risk-free asset instead of keeping the cash. By keeping cash you incur such a cost, whether there is inflation of not, and this means you should always keep as little cash as possible regardless of inflation. For example, if the inflation rate is -10% and the return on a (risk-free) savings account is 1%, then you are incurring an opportunity cost of 1% annually by keeping cash balances. If the inflation rate is 10%, you are incurring the same exact cost. So while cash balances can absolutely depreciate as a result of inflation, cash balances should represent a small fraction of a household's net worth anyway, since it's not optimal to hold large amounts of cash. Therefore a modest rate of inflation, such as we observe in developed nations, is never going to have a significant impact on household balance sheets, compared to other forms of depreciation such as the normal depreciation of physical capital (e.g. houses and cars).