A membership system will ALWAYS need a proper authentication model. I understand what you want but there will never be an option to remove the password field in the plugin because that will likely introduce security holes for everyone else using this same plugin.
The best option I can think of is the following:
On your registration page, instruct your users to use their email address as the password. So they will enter their email address in the password field. You are allowed to use any password you want.
You can edit the registration page and add a message there just before the shortcode.