Why would Taylor Swift mention "Love" in this context?

Rebecca

Here, "love" is a way to show who the letter was written by. It's instead of "from" or "regards." It's more affectionate. So I wouldn't use this formally with friends and acquaintances. I'd say it's common with loved ones, close friends, and family. She puts "love" here since it is written for her children. Ex: Happy birthday. Lots of love, Mom. Ex: I'm excited for your visit! Love, Henry.