Agreed on there being no impact on credit scores* - sorry if anyone thought that I was suggesting that there was!
My concern is mostly that I wouldn’t want any organisation to generate a credit assessment of me (obtaining loads of information from a credit reference agency in the process) without my explicit consent. As I say, this is probably a minority worry, but I’d be much happier with this happening after I express interest in an overdraft (or other credit product), rather than being done “just in case”. I feel much more in control that way - which is important for me with companies I choose to do business with.
*Yes, I know a credit score isn’t a thing 