YES, this idea is amazing, I want it implemented so bad!!! A friendship bracelet would be the perfect way to introduce this mechanic. You could unlock a best-friend specific greeting from that NPC, have them occasionally over for dinner or to come babysit your toddler when you and your spouse are out, buy them a drink at the saloon/invite them to co-play the arcade games in there like you do with Abigail, have them invite you to the movies or over to their place to hang out -- there are so many cute ways this could be done.
Man this really makes me really think about who I'd want that best friend to be. Probably Abigail would be the most fun Re: all of the above suggestions, but it'd make the mechanic super interesting if you could pick someone like Linus.