"A bank is a financial institution that accepts deposits from the public and creates credit." (WP).
The "creates credit" aspect is the central concept of a bank. A bank creates credit. Lending money is the core business model of banks. So something which doesn't lend money isn't a bank. The core concept of LN is that money in a channel needs to be funded first. A LN node doesn't lends money, so it isn't a bank.
Lending money is also the real problem, risk etc with banks:
If a bank lends out money to the wrong people, the bank can become bankrupt and all their customers deposits can't be payed back anymore which can create lots of trouble if banks hold lots of money. A LN channel only has the money which is funded first so it can't go bankrupt. People will always get their money back. There is no possibility of a bank run or economic collapse as with banks.
Also a bank can create "money from nothing" because of fractional reserve banking: The bank can lend money it doesn't have, needing only a fraction in reserves. That's what's known as "fiat money" and this has its own risks. With LN this isn't possible because channels needs to be funded with 100% of the money they contain, so also no risk here.
So LN doesn't creates "banks" again. LN nodes are no banks because the core aspect, "creating credit" is missing. People who repeat FUD like "LN just reinvents the banking system" simply have no clue how banks work and where the real risks are – or they use this analogy to push their agenda. So be aware.