In most cases, authentication is done outside of the application (SAML/SSO/...) - using apex accounts for authentication is not often done in production environments. It is best to split the authentication from the application altogether. If you start adding business logic to a login page you're going against that practice. Personally I think it is also overkill to display a login page to a user that doesn't have to authenticate. So far about why you made the correct choice.
Now why it failed. The documentation of apex_authentication.login shows that a "redirect" is the last step of the authentication process. If authentication passes then a user is redirected to the application home page, if it fails he is redirected to the page that is defined in the Shared Components > Authentication schemes > Current authentication scheme > Session not valid attribute. If you run debug on the login page that is the behaviour you can observe. My guess is that redirect will run before your own branch which is why it didn't work for you. It probably is expected behaviour.
Thanks @Koen, that makes sense and was what I was thinking, but being new to APEX wasn't sure how to 'find' the flow of the login process/request. Thanks for your help. and documentation link.