I actually like this as implemented by one of my banks. The 'pick a few letters' part of the login is pulled from a list of secret question answers rather than the password itself, and is presented after successfully entering the password.

So my password manager enters my password, and then on the next screen I am asked for the (for example) 4th and 5th letters of the street I grew up on. The requested letters change and the question is pulled from a saved list of question/answer pairs.

I am not aware of how the bank deals with accessibility limitations of this system.