How to use Keychain to Auto Login into Authenticated Websites
I'll talk you through this... what does a traditional keychain do? It organises your keys in a central location for you to access in an adhoc fashion. I'd argue that a keychain also mitigates risk of you losing any one of your keys accidentally. Food for thought... would you leave your front door unlocked with your keychain (including other keys) sitting freely in the key slot?

So the Mac Keychain is conceptually the same, it organises your cryptographic keys and mitigates risk of loss by securing it with your Mac password. Given that your password IS the entry point keychain, you got yourself a chicken and egg scenario. But anyway, I would sternly advise you not to pursue this idea any further. If somebody stole your device or remotely logged into it, and you had your system automatically logging you in, you'd be handing over your keys to a potential thief. In some ways, this might be even more dangerous than compromising your physical keychain.

So by concept, the Mac "Keychain" would be referred to in general IT terms as a "Key store", that is responsible for facilitating the storage of private and public keys. What you are asking for is essentially an "Authenticator" or an SSO (Single Sign-On) solution.

My recommendation: if you configure your everyday user account as a non-administrator, then you should be able to have it auto login to OSX. You shouldn't be using an administrator or Root level account for general purposes. If you get hacked or attacked by malware while logged in as an admin then youve pretty much handed over those admin rights to the Malware.