I have found in all parts of my life that I find more and more peace the more I let go. Not necessarily the material things; I used to save messages and voicemails along with memories and photos. It wasn't the treasuring of memories that was problematic but the actual ties to people and experiences that I was allowing to become too strong, too much of a focus.
I've found that be letting go of these connections, whether from old relationships or even current ones, I'm able to focus on the moment and what I'm experiencing now, who I'm interacting with now. Sometimes it's easiest for me to do this by actually deleting voicemail, deleting message chains, shredding or burning journal pages. For me, cherishing special memories but living in my now means letting go, and by doing that, I do let go of what doesn't serve me anymore. This doesn't mean I am ending every relationship, it seems I make more room for meaningful interactions if I'm not holding so tightly onto past memories and experiences.
When you were talking about blocking, it seemed like this is another "physical" way to strengthen personal boundaries but also to let go of connections that just no longer serve.