For Coinbase, is it mandatory to link a bank account or is it possible to use crypto only?
I don't think so, just read their FAQ;
1.
Why would I want a Coinbase Card?
The Coinbase Card allows you to spend funds from your cryptocurrency wallets available on Coinbase.
2.
Which assets can I spend using Coinbase Card?
Coinbase Card customers are able to spend their crypto from nine different wallets: BTC, ETH, LTC, BCH, XRP, BAT, REP, ZRX, and XLM
I haven't found anywhere to link your bank account. Since you are able to spend crypto directly so bank account shouldn't required. You may talk with their support or you may try to order your card so you will realized what is necessary documents required.