What is the use of the bank?
If you die and choose to return to the last point you saved at or last place visited (but not last autosave), it doesn't reload your last save; rather, you keep any progress intact, except you lose half your money. Money in the bank is exempt from this.
This has, I believe, been the purpose of banks since the very first Dragon Quest, and even some other games such as Pokémon Mystery Dungeon.