I think that banks can be trusted but that you just sometimes have to look out the most banks are okay and there are not doing anything wrong so..
have you ever noticed that the bank be a scam? I think only some of them and it occurs in privately owned banks. and not the government. so it is recommended to use the government's own bank. because it would clearly must be safe, and I believe the government
Most governments don't run banks at best they back them up with policies like savings protection, and to rescue them if they screw up, a banking industry owned by the government usually is a bad sign since it means some kind of nationalization took place which means banks are in a bad economic shape.
Yeah you should never trust banks with bad reputation and those who doesn't comply with government regulations. In my country the bank thats affiliated to my online wallet is registered to the governments account security on anti money laundering laws that gives protection to your money. We can trust a bank in a more strict screening and you should be more vigilant at all times when having transactions online and or offline banking.