For a perspective on opening account or artificial NRV with a bank to get a card.
Suppose you need 15 lac NRV with a bank to convince them (not unreasonable for premium cards).
For every 1% hit you take my moving investment to a bank from your current FD/investment you lose 1250 / month.
Suppose it takes 2 month for this process to complete and you take 4% hit in interest rate by moving money to HDFC/Axis saving account = 1250 * 4 * 2. = 10,000 loss (pre-tax)
This is higher than yearly fee of most credit cards after adjusting for fee payment benefit like vouchers/reward points. E.g. Infinia and Magnus only costs GST amount. I highly doubt banks will give cards like Axis Reserve / Amax Platinum LTF.
You can argue that you will get benefit of no-fee for long time for one time loss but cards get devalued quite frequently and will mostly be not worth it.