Absolutely not. Password reuse is already a problem now. What you are doing is actually enforcing password reuse. If your website could become successful enough, someone else will learn. At one point your roommate could build a website targeted you that also use this mechanism as you believed, but it actually passes what is transfered to their server to the roommate's computer, and then the original service.
Needless to say logging in using IP alone isn't secure. But you don't seem to understand this. Say you are working in a secret nuclear project, and no employee there would leak any of the informations. Does that mean you could easily tell everything to a coworker's girlfriend? Say you are running a bank. What happens if a parent sues you because their child steal their money (colluded or not)? And logging in using face recognition alone isn't secure. Combining two insecure mechanisms could hardly get you a secure one.
An obvious improvement to IP authentication is to use tokens (with or without also checking IP depending on situations). In other words, just keep them logged in. Why would they log out at all if they know they are in a secure location?
If the users are supposed to install some programs to use your service, you may also provide the option using face recognition on the client to "lock" the token string, as a precaution by the user. It probably won't be too useful in Windows. But for Android, it might be not that easy for a guest to root your device, extract the token string and restore your device to the original state in a few minutes without being noticed.
I guess you can also use face recognition in addition to passwords to improve the "security" in some special cases such as, you want to disallow users to resell their accounts to someone else, or want to make sure every user knows they are not accidentally using the wrong account for some reason.