Same happens on Safari, I feel I have to do the recaptcha a lot more frequently on Safari than on Chrome. I cannot find any serious study to back this though ...
The generated password is usually just random string and hard to memorise. If you need to use the password outside of the web, e.g. on telephone or in a physical office, then it makes sense to use a password you creates. This is similar to the "master password" used by password manager, you should remember it by heart instead of generating a random one.
Even this is a wrong move from the bank, I think that using password to have access to sensible service is not the safest way. Would be better if the bank can use some ID-verification service, preferably provided by the government independent company.
For me this was from my own frustration: I hate sign-up form and don't want to use "Login with Facebook/Google/..." either as these companies will have even more data about me.
I looked for an alternative to these social login buttons but haven't found any. I decided to quit my job as lead software engineer and created my own company that offers a social login solution that protects user identity [1].
The previous startup came also from another frustration (maybe because we are frustrated in France all the time ...) so my pattern would be to find something that bothers you (and hopefully others) and solves it.
Even if you don't have a Facebook account, Facebook still has your browsing history via the their SDK that is usually used to implement the "login with facebook" button. The sdk actually injects a iframe on the hosting website, allowing Facebook to know every time you go to this website.
I have the impression that people tend to turn to functional programming after spending a lot of time in imperative programming and seeing its downsides.