Thanks everyone for responses. I see how overdraft would be a problem with debit card usage. I think the main disadvantage highlighted by many responses occurs when
(a) without the protection, you *would* have seen that something did not go through (e.g. with debit card), but protection "hides" it from you, and
(b) account is used often, or one does not pay attention frequently enough that they don't see the fee hit the account until it's too late.
I think these are good points to keep in mind. In my particular case, the account I am thinking of does not have above two problems. It does not have debit card and is only used for periodic payment of ~3 bills / month. I also check for any weird activity on every monthly statement. So, hopefully, I would see the OD fee on the monthly statement. Finally, with direct deposit going into this account, even if I missed the OD fee hit on a statement, next direct deposit should cover incoming bills.
Given this, I think OD protection would be beneficial in my case since without it I think I would get hit with 2 fees (one for each side) for every online payment that is overdrawn and I would not know about it until I get the next statement either way. With OD protection, my bills would get paid on time and presumably I would get hit only by 1 side with fees instead of 2... Sounds about right?