ICICI Bank FD - does anyone see any potential concerns opening large sum FD account with them?

My parents are seniors and they have together saved quite a sum for their retirement. They want to put it in a FD account for annual withdrawal of interest. Does anyone see any potential concerns in opening large sum FD account with ICICI Bank? What other banks offer high interest rate and safety? Any other tax saving investment ideas are welcome. Appreciate your guidance. Thank you!