No you don't, or at least, no I don't. My bank has fees for depositing cash (more than x times a month), fees for withdrawing cash (even at an atm) and fees for holding my cash (having an account.)
Which country do you live in if you don't mind me asking, and are you talking about personal or business accounts? In the UK there are "premium" personal bank accounts that will charge you a (low) monthly fee, but you usually get benefits from these such as free travel insurance, and the fee will often be waived if you deposit £x per month. Transfers to most countries are free, withdrawals and deposits are free and two of my accounts don't charge for currency conversions or foreign withdrawals.
Traditional business accounts will sometimes charge withdrawal and deposit fees (especially on cash at the counter), and usually charge an (again low) monthly fee, but even in that sector you can find lots of accounts now that are essentially free.
I'm curious whether this is different in other countries.
But if you had kept the cash for that same amount of time it would have lost the same amount of value to inflation. You don't lose any more value from switching between levels.
You can deposit cash at a bank and get it back, but that's almost an exception.
Once you get into layer 3 it is harder and harder to get back to layer 1 or 2 without losing "some value" - gift cards being the most obvious example.