Absolutely. It's surprising that not everyone does this.
I have two bank accounts, each with a card and Apple pay. My "backup bank" costs about 3 euros / month for a simple payments account, savings and a creditcard.
My main creditcard is a separate Amex, but having a backup Visa card is useful also because Amex acceptance is still not great in Europe.
For less than 50 euros per year that's a lot of redundancy.
Are accounts free in the US? My impression was that you pay all kinds of fees for everything with most banks.
That 3 euros includes free ATM usage in nearly all of Europe and no fees on transactions within Europe. It's a lot less than what I paid in banking costs when I was living outside the EU.
If you follow the rules, you shouldn't need to pay for banking in the US. Different banks have different rules, of course. Many have a balance requirement, some have a minimum number of transactions per month to avoid fees, etc.
For ATMs, different banks do different things. Large banks have an extensive branch and ATM network, and often you pay a fee to use an unaffiliated ATM. Smaller banks often do rebates on ATM fees up to a certain number of transactions in a month. Some banks and more often credit unions (which are more or less banks) participate in ATM networks that provide a large number of ATMs worldwide. Some banks are in both the last categories.
The accounts are typically free, but they love to nail you on things like going overdraft by 1 cent or "inactivity fees" or other BS.
US Credit cards will only have fees if you get some super premium ones (and even then, there are often promos for that to zero out the fee temporarily or long-term).
I have two bank accounts, each with a card and Apple pay. My "backup bank" costs about 3 euros / month for a simple payments account, savings and a creditcard.
My main creditcard is a separate Amex, but having a backup Visa card is useful also because Amex acceptance is still not great in Europe.
For less than 50 euros per year that's a lot of redundancy.