No doubt people have discussed the concept. If I were a navy looking for funding, or just another use for an existing sub, I would definitely propose it. But I don't see the practicality of going through all that effort for rather limited gain. If this is an enemy cable, it will be encrypted. If it is a privately-owned cable (internet) then it can more easily be tapped on land or via a standard ship. I suspect that even an enemy cable, if it is in public waters, could be spliced far more effectively by a surface ship.
Once the tap is in place, how do you get the information from the tap back to HQ? The sub won't have the manpower and computers needed to gain meaningful intel from such a cable. Getting the data back to shore would require either another cable or an in situ recording device a la ivy bells. Recording devices would both delay any data by weeks/months and limit the ability to insert data, an essential task when attacking encrypted connections.
Once the tap is in place, how do you get the information from the tap back to HQ? The sub won't have the manpower and computers needed to gain meaningful intel from such a cable. Getting the data back to shore would require either another cable or an in situ recording device a la ivy bells. Recording devices would both delay any data by weeks/months and limit the ability to insert data, an essential task when attacking encrypted connections.