It's a good place to hide or accumulate money without the worry of someone taking it by battling you.
But it takes 20% fee so it's better to "bank" your money in tutors and sell them later (unless you're getting stripped= stripping is someone/ppl hiring all your tutors to expose your money and get it cleared by attacks). If you get stripped, either upgrade, if you can, either buy defense and attack items or use the bank.
If you are in war or PvP , the bank is a great way to hide cash , even though there is a 20% deduction in cash, when cat cafe exsists you get it? but anyways its there cause back in the day it was useful.