Comment by TFNA

Maybe that works in the some countries, but among the 3-4 mainstream banks in my country, making that threat when you are anything less than an unusually high earner by local standards (and perhaps a customer of ancillary investment services) is just going to be met with "Fine, we'll close it then." You might be overestimating just how much banks need any one average person's custom. Also, by local cultural standards, making such threats to a business for the sake of obtaining better customer service is over-the-top Karen behavior, so you have already lost when you do that.