That advice you're giving there is actually kind of dangerous & misleading.
It's still wise to at least consider the possibility of a bank failure, qv Northern Rock.
Grandparent comment's advice about keeping an overseas investment is wise, too; as a Brit I've not regretted having US investments.
Most industrialized countries have insurance of bank deposits up to a certain point. So even if the bank goes poof your savings are still safe.
It would simply be prudent to have money in more than one bank (or credit union), as if something bad happens then things may get chaotic in the short term.
A second account also helps with IT problems:
* https://en.wikipedia.org/wiki/2012_RBS_Group_computer_system...
* https://www.theguardian.com/business/2019/aug/27/natwest-and...
Hopefully you don't mean in a bank? If history is any guide that's useless with capital controls initiated before the public even gets whiff of it, see Greece and Cyprus 2008. A bolted-down safe in your house seems to be the caveat on such a statement. Money in the bank simply isn't yours and far too many people don't realise this.