Is the lack of information on customer behaviour good for banks?
Basel II opened the possibility towards "your individual interest rate" by allowing (and encouraging) banks to use more advanced methods of estimating Credit Risk, individualizing even, customer-per-customer, for example using Advanced-Internal ratings-based approach.

This means that the banks can lower interest rates towards clients that score better according to these presumably more sophisticated methods of credit risk assessment. They are not obliged to do so (to the degree that interest rates are determined by the interaction of market participants and not decided by the state). On the other hand, by making credit risk assessment more accurate, banks can select the customers with good credit ratings because this, in the end, lowers their overall credit risk exposure and ultimately, lowers also the obligatory capital that they must hold.  

So indeed, individual credit rating and individual interest rates may increase the competition among firms and bring contractual interest rates down, reducing the banks' nominal profit rate -while it may keep intact the actual profit rate, since credit risk (and so, statistical losses) will also go down.
Moreover this may lessen the burden of capital reserves. In some cases (and I would say, in the current situation), banks may even care more about the latter than the former.