Banks that issue a card with no account condition
Citi Bank Handlowy historically specialises in clients who want a card without moving their account. Citi Simplicity and Citi Premier Miles are issued against income proof. UniCredit (operating in Poland through VeloBank) runs a similar policy on UniCredit Standard. VeloBank issues Visa Standard with no current account either, but requires an insurance policy at 9 PLN per month.
What the bank wants in place of an account
Income statement from the employer (or a PIT for the last tax year). ID document plus PESEL. Statement of monthly outgoings (rent, other loans). BIK check, standard everywhere. Cards issued without an account usually carry a lower starting limit (1 500-5 000 PLN) and an RRSO 2-4 points above cards issued to account holders.
When this route actually makes sense
You already hold a good account with another bank (mBank, ING with specific perks) and don't want to switch. You travel often and need a card with good foreign terms (Citi Premier Miles, UniCredit). You work in a company where the salary lands at a bank you don't want a card with. These are scenarios where 50-100 PLN extra per year buys real account-card independence.
Pitfalls of cards without an account
Paying the instalment requires a transfer from an account at another bank, so remember the title and the card's account number, since a mistake means money to the wrong place plus late interest. Most banks don't charge for external transfers (usually 0 PLN, but check the table). No automatic direct debit from an external account, you have to remember yourself. A late payment costs 80-150 PLN plus interest.
My take: when to take this path
Stable job, good BIK, awareness that you remember dates, Citi Simplicity without an account is a fine pick. Every other scenario (unstable income, weak BIK, no habit of tracking dates), worth opening an account at the bank that issues the card. Automatic debit from the same account removes the transfer-mistake risk.