Is credit one bank a good credit card?

The Credit One Bank® Platinum Visa® for Rebuilding Credit is a pretty good credit card for people with bad credit who don't want to place a deposit on a secured card. The Credit One Platinum Visa can be worthwhile because it offers a $300 credit limit, rewards, and the potential for credit-limit increases.

Can a Bank refuse to close my account?

No. They can't refuse but have the right to convince you to change your mind if your account matters them ( it happens rarely in PSU banks) If all your liabilities are cleared then bank cannot refuse to close the account. No Bank can refuse to close your deposit account and even loan account if you are repaying all dues with interest.

Is it necessary to close the bank account?

Whatever the outcome, it would be wise to formally close the bank account and cancel the credit card. It is important to get this confirmation in writing to avoid any issues in the future but be aware that the bank has the right to charge a fee for this small service.