I don't think I ever have my browser not open. I use something like four different computers, not including mobile devices, and appreciate the central copy without having to think about syncing it. I don't worry about setting up scripts on my local machine or updating my local plain text copy so that it can be searched. For the archiving users, they don't have to manually save the files of each website they'd like to search later.
If you believe you can do bookmarking better and free, then do it. If it matches what I'm using Pinboard for, and is better (and doesn't use Dropbox), I'll switch.