I'm aware that I'm perhaps atypically vehement on this point of view - I refuse to delete old phone numbers, and have had a tough time removing frenemies/old flames/former friends on Facebook and other social media simply because, although I may not have a connection to these people now, I'd prefer to know what they are up to if I so choose. Except in extreme cases (a particularly poisonous former friend, a particularly painful and frequently-thought-of old lover) when I can't help myself or it's better to excise the drama, I opt for the ability to have knowledge over completely cutting someone out. Part of this is because I want to prove to myself that I am able to not interact with them (once a relationship is ended, for instance). And a large part of it is also a raving curiosity I've always possessed.

I very well may be in the minority here and if it comes to that I will accept it, but for me the mute function would lose its functionality, unless in an extreme, inescapable case of personal harassment.