You're assuming the money is invested only as cash in the bank. It's quite possible to make considerably above inflation with other investments, and anyone with that amount of money is very likely to have a range of investment types.
How much of that theoretical nest egg would you risk to investments? 70%? 30%?
Inflation chipping away your savings is a given, but investments that match or beat inflation have no guarantees.
How much of the savings would remain after 15 years? Would you still feel secure going back to work in your 16th year with no money in the bank for your car/home/health/life?